It's also hard when you're looking for a gf or wife, and all that flocks to you are "the darkly inclined." Some women ruin everything (just the "pretty" goth ones). It shouldn't be about complete and total fiction (i.e. Frankenstein, mad scientists). It should be about the real world. I am SLOWLY getting back my interests, thanks to a co-worker, and my brother.
@@the11thken That's another reason. In order to make any subject learnable, you need a teacher that cares about students. Not one that loves to be dictator (yells, writes anyone up), not monotonous, and not scary. What I've been all along is: it's not the subject itself, it's the people. That's true for anything. I love chemistry, biology, and physics. It's the instructors, teachers, classmates, peers, etc. that make or break interest.
Back in 2018 I stopped everything I was doing and just sat down to study and master basic arithmetic and algebra for months. Saved my life. Before I had trouble converting between say decimals and percentages, or dealing with some more involved equations with lots of fractions, powers, and so on. Had trouble with graphing too. I just practiced everything as much as I can, mixing the different skills, testing every scenario, using tools like desmos and geogebra to help me experiment with the concepts. Eventually this made algebra a trivially easy thing to do. Best thing I've done in my life tbh, since a lot of my interests are math based.
@@albirtarsha5370 my main motivation is that my interest are really math heavy (astrophysics and machine learning), I told myself if I keep struggling with fractions I won't be able to deal with physics any time soon 😅 so I had to conquer it. If you're a physics teacher you can remind your students of their goals, even if the goal is just to graduate with high grades, and especially if their pursuits involve math, remind them it's always worth it to master the fundamentals, it's a one-and-done thing that will always serve you, better to struggle with just the physics concepts than to struggle with both the physics AND the algebra right? That was my logic 😅 But unfortunately I only did this as an adult after leaving school. During school I just didn't have the time to do this even tho I had the interest, I collected my math textbooks since like 5th grade and always had the plan to set down and really put together everything I have studied and master everything. But unfortunately I just never found the time as a student in K-12. And now since I can't afford higher education I just continue teaching myself my favourite subjects with plenty of time to invest in them.
@miryasin7930 ALEKS online is a good platform for learning math. It is adaptive, so it only makes you do enough problems to learn each lesson. The cost is $20/month, which is cheaper than paying for a tutor.
I know Calculus well but for me it's harder to get to the maths part than actually do the maths. So understanding the problem and applying physics to it is where I struggle the most.
A thermometer has a measurement system. Before there was one, there wasn’t one. Physics is like trying to tell a temperature with out the measurement system on the thermometer. Every new physics calculation is adding another measurement system akin to the one you can find on a thermometer or a ruler; or a calculation that brings math into proportion with a previously known measurement system. Wave function is one, spin quantum number is one, E=MC2 is one, Cm & Meters is one. Yada yada. Once you understand what they mean and where they apply in terms of scale you understand the system. You do not need maths to do this. You need maths to discover/prove it but it doesn’t mean to say you need maths to go in the direction of discovering something new. For example, I don’t understand the maths behind thermodynamics but I understand thermodynamics enough to help not crack my windscreen when it’s frosted over. I can use this as an analogy to describe phenomena at a molecular level but it doesn’t mean to say I could write it down in an equation. I think we have the same problem. 😂
This is normal and it doesn't have to do with your understanding in physics. You're solving a problem, and THAT is the hard part. Even if your understanding of physics is really good and you have a great knowledge of math, it can still be really hard to solve problems that you have never encountered before. Just remember, that even the easiest problems in math, took many years to be solved even by great Mathematicians! And how can you become better at solving problems? Just by practicing and seeing as many solved problems as you can, it's the only way!
Sometimes it's the math, sometimes it's the physics. People sometimes get caught up in the whole idea that physics is physics and not math, that they end up using poor and oversimplified mathematical models for situations that require more sophistication. Spherical cows is a common physics joke. That's where you have to give engineers respect, because they are actually the ones to do detailed fluid and finite element simulations using programs like COMSOL or ANSYS to really analyze the details. Why physicists don't do this is beyond me. It's the same way it is baffling that chemists aren't the ones studying elementary particles but rather physicists are.
The basics is exactly what's in the video, algebra. Just get really good at manipulating equations, everything will make much more sense if you can follow the derivations. You might also start learning polar form vs Cartesian form, how to convert between the two (that's basically vectors). Knowing integrals is useful for understanding derivative, essential if taking a highly rigorous physics course (major specific intro and above). But yeah, basics=algebra
My secret? after getting an 'F' in upper division Mechanics, I got a student job tutoring physics. I really had to rework my understanding into simple and consistent explanations. I got more out of it than those I was teaching. Coolest thing: The guy who was struggling, but actually kept showing up, and got better and better. He never tried to "just get the answer". Good Times! Never Quit. Find the most do-able way to "not give up" and succeed. You'll won't regret success.
Physics is hard because it takes experience and practice to learn everything. You can’t simply walk in and be really good at it, you need a good teacher. The issue is way too many physics teachers either won’t give you the time of day, or they are just so busy they can’t give everyone enough time.
Exactly, the teachers must be creative cause there's lots of abstract concepts in physics. Students cannot just sit in the class and imagine everything.
I tried to memorize patterns of procedures of solving physics problems when I was undergrad and eventually realized that it's impossible and you had to be flexible with Maths. Then through a few years I began to see more abstract patterns that I often encounter and I finally noticed IT IS NOTHING BUT ALGEBRA that deal with patterns. Now I'm preparing for phd deffence. Wish I noticed a bit earlier.☠️💀
Can you please elaborate on what you mean by 'it is nothing but algebra that deal with patterns'? In the context of undergraduate courses in maths, physics and engineering.
Hi, thank you for this analysis. Physics is hard for many students not only because of gaps in their knowledge in maths or because of lack of practice, but also and probably mostly because developing a clear and proper representation (or mental picture) of the problem at hand is not as easy at it seems. As a teacher of physics, I see that a rather large proportion of students in a cohort find it difficult to develop their reasoning. Proper reasoning requires a good knowledge of the notions discussed during the lecture but also an ability to picture mentally the studied problem. This is particularly true for thermodynamics when a key step for problem solving is establishing the correct energy balance.
Yep, there are lots of reasons physics is hard! Visualizing in 3D can also be tricky (related to your point). I am bad at that. I can do it, but I have to really stop and take a minute.
@@emar22111 Same for me! Though I wanted to become a physicist, I always was better at mathematics. I started uni in a maths program, always keeping in mind a transfer to a physics program at some point, which I did in third year as I felt more confident that I could at least manage the formalism of quantum mechanics, kinetic theory, mechanics, etc. However, it proved extremely difficult for me to adapt to the physics curriculum: the way they do maths in physics is not rigorous and I got frustrated, and my vision of physical systems was always blurred. It took me years, up to PhD level, to adapt and change my habits to become a physicist. Still, I find it easier to teach the mathematical formalism than to teach how to mentally picture physical systems and processes; cognition is something quite personal and there is no recipe that works for all.
You are not the only one. In maths you manipulate symbols. In physics symbols have meaning and it is not an easy task to work with symbols having physical meaning. @@emar22111
As an ex-physics professor I know the answer to this question. I’d like to say my college teaching experience is why I know the answer, but honestly my years of helping and attempting to help my “pre-med” or “other” friends and acquaintances deal with their first physics and calculus courses already taught me where the essence of the difficulty lies for some people. The answer is that Physics, and also Calculus, are very often the first place where a whole LOT of students come up hard against the requirement to turn actual understanding and first principles, rather than rote memorization, into practice. It is the first place in our present educational pathways that many students come up against the a brick wall that is very hard to penetrate with rote learning. Yes, students are exposed to baby versions of this kind of “thinking on your feet” much earlier, like proving theorems in geometry. And they can fake their way though an imitation of the process in algebra and pre-calculus by memorizing and implementing a small set of rules which they are then taught to apply by rote. But the rubber really hits the road in Physics, Calculus, and especially in the required pre-med “Physics with Calculus” - the horror, the horror! For many students the memorization-heavy, analytical-thinking-minimal method they have used with great success up to then fails at this crucial juncture. “Fails” is perhaps too strong a word since absolute failure would probably have been a gift at this point. In reality it is more cruel that that - the memorization it takes to avoid fundamental understanding, the FAR easier alternative, ramps up exponentially until it reaches an absurd level forcing a crisis in people that haven’t yet had to face such things previously. An (over) simple example - the absurdity of trying to memorize the “formulas” (x = g(t), v = h(t) ) for every trivial mechanical question involving Newton’s laws rather than learning how to apply them ab initio. Anyway, many of the students that are freaking out at this point are experiencing the failure not of their intelligence, but their highly developed, and by this point time-tested and proven memorization-heavy “learning” (and it is not an exaggeration to call this UNDERSTANDING) techniques. This problem is something very hard - leaving aside that teaching students HOW to think is not really in the job description - for the professor to simply “teach” the student out of. I know from experience the disconnect when a student that wants “help” but is only prepared to accept it in the form of an answer to “tell me which formula I should memorize?” The frameworks for exchange of information themselves are mismatches - or aptly, “the matrix is something one cannot simply be told about, you have to experience it for yourself”. 😂 For a few or the students, the ones that are already prepared, this is a point they experience as a kind of liberation. For the others, especially some of the pre-meds that are “forced” to endure this trial - coming in to the class with an “I’m gonna hate this, but I have to pass and hopefully get an “A” to get into med school” really doesn’t help - it can seem like nothing makes sense anymore. To have this occur at a time when nearly all of these students are also experiencing a new environment, and new social pressures, well that is a recipe for trouble!
In my junior year of Chemical Engineering I tutored a older nursing student in organic chemistry including some reactions. She was going into nursing from a clinical psych background. When she was able to visualize in 3D and notice things like where a slight charge would be she finally turned the corner. She no longer needed the models. She finally understood why there was more than one product of a reaction and what the probable ratios were. That slight charge thing, that was a tough one to get her to. She understood an electron has a charge, and that is the unit of charge, so how can a compound be slightly charged at different places. It was a victory for both of us and one of my greatest achievements.
When you deal with problems in physics, you have to make sense of the problem and apply concepts to a solution in mathematical terms. You have to build the argument from scratch. This is by far the most challenging part.
But don't students get a lot of that in word problems? That's where they take real (if rather contrived) world problems and apply what they just learned.
I think it comes down to learning preference. In high school, typically the people who take biology (lots of memorising) don't take physics (very conceptual and math heavy), and vice versa. Chemistry is the "middle ground" (both memorising and conceptual, with mostly arithmetic math, and basic algebra) where both physics and biology students take them. If choice is available, students who take all three of those sciences, or those who take physics and biology, are unicorns.
Chemistry ? Nobody wanted to be my Lab Partner. After a few classes and a "Jaws themed 'ear-worm' infestation", I realized I was surrounded by Pre-Med students who (by the Junior Year) knew each other. The Kiss of Death was "Grading on a Curve". I realized I was the likely to become Chum for the Pre-Meds. I dropped it in favor of 'Fencing'. From frowns to smiles! Best-Decision-Ever.
I still remember when the lightbulb came on in a physics class in engineering school, as some problem involving a cone and an integral was being considered. It was like "calculus can be tied to a physical problem." It was the first time we used calculus outside a math class. I agree with you - tying it to the real world can make it easier for those not as good at the seemingly abstract mathematical theory alone.
I've always been pretty good at math. When I took relativistic physics I got a reality check on how theoretical I was capable of thinking. Just meet with your physics prof during office hours and send some emails back and forth. The more he/she sees you are trying the more likely (he) will be to help you understand the concepts that he will be testing you on directly. I failed the first test (30% of our grade) and panicked but utilized every office hour session available to study directly with my prof. I ended up acing the midterm (30% of our grade) and think I got a B+ on the final (40% of grade). Ended up passing the class even though I wasn't happy with my overall grade. Still my most memorable class ever with the only one even coming close being differential equations.
It's a good advice and that's also how I got a good grade in calculus. But you have to have a teacher who's willing to be patient and my current physics teacher is anything but...
Everyday, I'm amazed again and again at the care and dedication you put out in your lectures. Sir, you are probably the most brilliant and enthusiastic physics teachers in the world.
knowing those little short cuts is helpful like knowing that anything in a denominator on one side can simply be moved to the other side as a numerator so 1/2 on one side can by moved to the other side as 2, 1/x on one side gets moved to the other side as X, etc.
Great video and as an engineer and psychologist, I agree with everything Hafner said. Going deeper however, to be successful in any rigorous academic pursuit, developing critical thinking skills are an absolute necessity. It’s the basis for all logic and math. Developing CT skills takes a LOT of effort and time and does not come naturally to most of us. We tend to believe we are more rational than we really are, so our expectations that maths should be easier to learn than they actually are are usually wrong.
Yes, for sure. This video was made as an intro for a freshman mechanics class, so it is somewhat out of context here on YT. As students move on from freshman classes, there are new challenges like CT and many others! ;)
Yup! I also think that approximations trip up students sometimes. Trained physicists have a good eye for the essential features of a problem and can drop some of the details to approximate. Students can sometimes find all the information overwhelming and not know where to start.
They don't learn approximations in high school. In some cases such as the small-angle approximation in the motion of a pendulum, it is the approximation that makes it possible to solve. I would make the students put their calculators in radian mode, and then have them calculate the sine of .001, .01, and .1. The real logic or the small angle approximation comes from the Taylor-series expansion, but a simple practical demonstration is probably more helpful.
I teach both physics and calculus and I agree with you 100%. Math is so important. However, I had students who had all A's in math, but did not do well in physics. They just couldn't grasp certain concepts. I think the reason is that in physics no two problems are the same, you can't just memorize some steps on how to solve a problem. In math, including calculus, many procedures, like the product rule, can be memorized without even knowing the proof of the formula using limits. In physics, you can't just memorize that the net force is mass times acceleration. For a simple example, like the Atwood machine, students need to be able to draw a free body diagram and to add all the forces and then solve for acceleration by using algebraic methods like substitution or elimination. That requires a skill and critical thinking.
I taught Engineering Mechanics to first year Engineering students, and that's like physics on steroids. An elementary issue of course is understanding vectors and how to do calculations with them. Another issue, which is why engineers emphasize Free Body Diagrams is understanding the point of application of the force. I find that it can be difficult to convince students that they need to use vectors, but it's even harder to convince them that the point of application of the force is important. It's all kind of detail-based and pedantic, and people don't embrace that. They want it to be easy.
Exactly this! I found math in school easy bc all i had to do was memorise the steps and put it into a calculator but i struggle with physics a lot more because you actually have to understand what your doing to be able to answer a lot of the questions
One of the problems is that some of the things and connections that can be memorized, abstractized, related to similar concepts or "simplified" in terms of idea, start only after you are already very good at math 😅😅 So, before you reach that level, it's often already "too late", as some people never reach it, already graduated or go for PhD+, which is vast minority 😂 It really takes time and effort to not only get much of skill and knowledge, but also "mathematical intuitions" in certain types of tasks, so you can easily do "educated guesses" etc. It's really good that physics helps create this intuition!
I remember how our mathematics teacher in secondary school led us to a situation where I felt the need for differential and integral calculus. When I started to study electrical engineering, the calculus already made obvious sense and was something natural but this time in a technical rather than a theoretical-abstract context.
For me it wasn’t the math. When I got to upper level physics, it was setting up the problems. I’d either miss key info or neglect a key piece of physics involved in setting up the equations
The best way to learn physics is to have 1000 questions from the simplest, gradually getting more difficult. Memorise your formula for each topic. Practice writing out or telling someone else your understanding of the concepts of each topic. My physics professor always had the whole blackboard full of questions and our lesson was doing each one and he would also talk about the concepts as we went. I remember after attending my first lecture with him, I was so excited to go home and do the assignment for the week. Who gets excited about physics?
Yeah sometimes I worry we go straight to the "deep understanding" problems, when some folks need to start by doing routine problems to get used to the formulas and concepts.
I was a lost cause at math. The deputy headmaster (Ernie Enderby) gave up his lunch hour to educate me one on one, with no distractions. X & Y meant nothing to me, so Mr Enderby brought in a bag of apples and oranges and used those in place of X & Y so that I could follow, see and visualize the equation. I failed the exam. I did sit a retake six months later, I passed with the lowest grade. Other subjects I passed easily never gave me the happiness of my math pass, it still pleases me to this day. I should have gone back to the school to thank Ernie Enderby but I was still young in1973 and had my head up my arse. Thank you Ernie Enderby for giving me your time and effort.
It's wonderful to hear that Mr. Enderby went the extra mile to help you understand math and that you eventually passed the exam. Teachers who dedicate their time and effort to support their students can have a lasting impact on their lives. While it's never too late to express gratitude, it's understandable that you were young and didn't think about it at the time. Nevertheless, it's great that you still appreciate his efforts and the positive effect it had on you. Teachers like Mr. Enderby deserve recognition for their dedication and commitment to their students' success.
Yeah,I've also have difficulty in math,I'm dyslexic and have add. So,I always hated math, however one tutor, Mrs Smith,now a principal was so patient with me,sometimes,I even liked math,learning from her. :) However, another math teacher,was so shocked at my wrong answer,he cursed at me,in front of the entire class. So,in that class,I never asked for help again. I actually came here to understand my boyfriend, who is always talking about physics. So, it's not like he's speaking in foreign language he's speaking to me anymore. 🤪
This is subject very dear to my heart .... at 85. I struggled, came close to failing sooo many math classes while a youngster in jr. and high schools. THEN I all but accidentally was taken under the wings of a superb collegiate professional level math professor ... WHO KNEW HOW TO TEACH MATHEMATICS.!!! Within TWO months ... with totally focused, dedicated teaching, he moved me from the basics ... to third order integrals!!!! The man was like magic. Unfortunately, due to other circumstances I was not able to progress into the professional worlds of science, as I so dearly wished to do. However, the event, PROVED so clearly, that the quality of teaching, and instruction, and the overall approach to learning advanced math, is EVERYTHING! (Assuming of course, the student has the 'raw materials' and an eager attitude to start with!) Aside from the qualifications of the instructor, perhaps too, the surrounding atmosphere and sense of importance is also crucial to a successful life in mathmatics and high level science. Inept, or truly unqualified instruction in math ... is a guaranteed path to failure.
I failed physics and ended up with a degree in mechanical engineering. The only reason I passed was because the whole class did so bad, the professor curved final grades like crazy. The more you do something, the better you get at it. Keep getting better at math, keep doing problems, keep pushing yourself to understand and you’ll get it eventually!
The system isn't the greatest. It's good for making connections.. it's required for measuring people's understanding.. I wish I didn't go to uni after highschool and just read books and self reflected instead of 'keeping up with the jones'
I like physics for its real world applications and how it is so awesome to make us understand the world around us. But I don't enjoy doing calculations that take too much thinking and I cannot manage to like math classes. It's not a horrible time but I am only pushing through it. So I went for chemistry because it also allows me to learn, in a slightly different way, how the world works (which I tend to prefer, too) and generally uses less maths.
For me it was always about finding a way to represent the problem. The first week of physics was always about converting units from one to another, and it was strange to me why that only happened in physics class. Later in life, as I challenged myself to do some really complicated programming, I started to appreciate the skill of representing a problem in a way that allows it to be solved. But that doesn't mean I ever really got good at physics at all.
If you can wake up at 8AM on a Saturday and are willing to work all day, it begins to get _less_ hard. If you can do that again on a Sunday, even better. And if you aren't good at staring at the wall, you will struggle. Coffee, walls, and time are the best way to do physics. Oh, and scratch paper - don't be afraid to write down every single thought you have, every little intuition, every little hunch, or otherwise seemingly meaningless bit of an idea. Coffee, walls, time, and scratch paper. If, however, that's not how you plan on putting bacon on the table, then it's up to you to figure out your own priorities. P.S. Never show up to a math/physics class tired. Nothing will stick inside your head. Experience taught me just how important this is.
I think many in calculus courses still suffer understanding the algebra, and those in algebra have a hard time doing basic math. This is as courses usually just need a C- to really move forward and those exams are always curved where you might only get 3/10 questions correct and yet "pass". So the student is unprepared to deal with calculus-based physics where the teacher is usually unlikely or not fond of teaching you the underlying math.
This reminds me of our polytechnical first year, electricity being explained using both calculus (magnetism around a conductor) and alternating current circuits solved using complex numbers. Both weren't yet taught in maths. So we were taught stuff with methods we didn't know yet. Only at the end of the year stuff came together, but by then the derivation was already passed,.
I think students think physics is hard because we wait until 10th or 11th grade to teach them what we'd like them to know when they graduate high school. If we started teaching physics in 6th grade, and taught them some each year, they wouldn't think it was so hard. We teach kids "English" and "history" each year until they graduate, but we expect them to absorb all of physics in one class in one year. Our watering down math and science in the early years causes our students to need a huge catch-up phase at the end.
While I agree, I have to say that, at least in the United States, we do teach "Science" classes all throughout Elementary and Middle School. And in High School students are required to take Biology, Chemistry, and Physics so it's hard to have just more pure Physics class requirements.
@@AB-et6nj Well, science classes like Biology, Chemistry and Physics are not required in my state. You have to take one science class to graduate. If you wish to go to college, the other science classes may help you get in and they would likely help you pass their college level classes once you're there. The science I was taught before 10th grade was hardly worth my time. It was like "science for history majors".
I think that math is a more applied science than math and what I mean by that is that you could get quite good at math without understanding it very deeply on the other side it would be hard to be good at physics without a good understanding of the topic. At the same time I think that Physics is hard to teach since it's hard to understand, so you're kind of in this infinite loop, that's why being good at math isn't enough to be good at physics.
Something like 40% of the lecture time in the first year of my physics degree (Imperial College London, 1989) was devoted to equipping us with the mathematical toolbox to handle the remaining 60% of actual physics, to the extent that the lecturers were drawn from the mathematics department. It wasn't just calculus; there was a strong component of linear algebra, but we certainly were hit pretty early on with differential equations, Green's theorems, complex analysis and numerical quadrature methods. Now I have a bit of downtime I'm finally teaching myself Lie algebras, just out of interest and 30 years after the fact.
For me, pure maths has been something that I struggled to learn, some concepts in physics intrigued me when I was a kid, I think it's time I should start to learn maths again, it's fascinating, I need to know how these things work.
As an engineering undergrad, I can attest to the fact that the biggest thing college has taught me is the algebra of the matter will lose you the most points. Doesn't matter where.
Algebra really is the whole of physics, along with the elaborate problems told in a story to set up a problem. I think a lot of people get lost in the story and lose focus of the goal. What are we solving for? Or basically why are we here, why am I reading this problem? Working backwards helped my physics so much
For me its the opposite. Completed all the math classes in undergrad, but the department's lack of teaching made my math worse, all I learned were derivatives, integrals, and how to regurgitate anything past calc 3. in physics now and applying things/connecting dots is extremely difficult because the problems require context and aren't as concerted/braindead. I honestly feel like college made me worse at math aside from learning integrals. Could also be burnout, I'm a working first-gen student making ends meet.
For me, when getting started with mechanics for AP Physics, I would say the math was not the issue, but rather how to apply the formulas, concepts, etc to a specific problems
Does applying the formulae to solve questions not encompass math? I think you mean algebra and manipulation of formulae were not the problem. I study maths in University, and we barely even consider plugging numbers into a formulae to be real maths. Real maths is more about understanding concepts than knowing how to manipulate an equation algebraically.
@@epicchocolate1866 yeah my comment was a little naïve. I mean I had seen a glimpse of that sort of math in that class (Physics C=calculus-based), but can only imagine how much more interesting it gets
I graduated from high school in the 60's. I was taught in my first year of Algebra to use what is called the transportation method. Some time after that, maybe years, that I learned the properties of Algebra and realized that the transportation was just a "short cut" to the application of properties. I went on after high school to earn an engineering degree from a prestigious university. I now teach upper high school math and Physics and find students are not as proficient because they were taught the application of the properties to solve Algebra equations. This is somewhat frustrating. I believe we should go back to teaching the way it was taught in the 60's.
My elementary and middle school math foundation was never good. I always asked a lot of why? why? why? questions in all my classes, not to be inane or talk for the sake of hearing my own voice, but because I wanted to get to the bedrock of truth. I was usually told to shut up and ne quiet, and thus I did terrible in math. Actually developed a real fear (not just a dislike) for it based on the hostility of my teachers. They demanded I just listen, memorize, and do the homework but didnt care if i struggled. I never learned the logic underlying machinery of WHY, say, the quadratic equation worked so I could do examples in class but never the homework. Algebra is where it falls apart for me and i know i can learn but feel like i need to go WAY back to basic arithmetic so I have underlying understanding to be prepared for algebra
I'm currently doing my masters in mathematics. In order to truly grasp certain proofs and concepts, I've been making use of memorization and high-level learning. My point being that those two have a role to play even in the technical disciplines! Since math is necessarily very detailed, it's easy to get lost. One might have understood every detail of a proof, but done so at the expense of the bigger picture. Recently, I've been trying to approach proofs in a two-fold way. First, I study them at a high level, and try to understand the main ideas. Then, on my second or even third reading, I worry about the details.
Right, I've often wonder if the approach of teaching (and even going through) proof is a good way to teach/learn. Yeah, you learn (hopefully!) how to proof something or derive something from first principles but you may lose the point why something is useful and even forget (by the time you are through) that there is this or that method (don't know the correct English word) that you could apply in this or that case. In my youth (before computers) complex arithmetic was used to solve certain electrical circuit (AC) problems. I often complained that I've never seen or heard of a complex or imaginary electricity/electron/current so why do I have these in the equations. Took me years to realise that it is (well, today, it was) a handy MATH tool to deal with sinusoidal signals.
@@Axel_Andersen You're not alone! I often take courses, pass them (though certainly not always), only to understand the point of them a number of years later in a completely different context.
4 years of physics olympiad veteran here, yes, algebra is actually something you want to do as efficiently as possible Physics based calculus arent usually tricky. And even it you get into distribution type of stuffs they aren't as hard as those you see in Mit integration bee
Trust me, it gets way more complicated in collegiate physics (let alone grad school). Most of my professors actually give us integration tables. They don’t care about our ability to integrate, they care about our ability to comprehend, digest, and apply complicated physical concepts. We use math, sure. But an actual education in physics goes WAY beyond that.
I am fascinated by physics as applied to astronomy and have great respect for those who can do the math. And this is from someone who went as high as multi-variable calculus.
Sir, you made a very good point. But, one more thing that I'd like to add, that is, I was extremely good at Math in high school, but I was worst at Mechanics, especially Newton's Laws of Motion. I would always face problem in making Free Body Diagrams, and would always mess up where or how the forces would be acting. For example, cases of systems of pulleys where there are horizontal blocks affecting the motion of a falling block, or cases where a man would be in a self-lifting elevator - they troubled me a lot when I solved in conventional ways. It turns out that, its more about certain basic knowledge of Physics or physics common-sense that students usually lack. Most teachers tell that Physics is totally common sense, but infact its really not "totally" common sense.
Great point, I think the moment physics first "clicked" with me was when I understood why mass isn't mentioned in some formulas that we're usually told to memorize. Like aside from understanding how integration of force gives me momentum, it's when equation ma = mg and just doing algebra that I was like "ohhhh so that's where the mass gets cancelled out before i go down to finding position and velocity, THIS is why acceleration is the same regardless of weight", something I was always told in highschool but never understood
One of my math professors once said that mathematicians don't always care about applications, and I have always found that mindset quite interesting - it seems strange that someone would devote lots of time on something without caring about why it is useful, but I guess that mathematicians generally view math as a prepared "toolbox" for whatever stuff that people might need.
@@lauterunvollkommenheit4344 I knew when I called math science there was a problem as it would be better described as the language of science. The world functions without humans counting and measuring it.
This is the first of your lectures I've seen; I hope that someone, at some point, has mentioned how much your cadence, intonation, and educational intent is reminiscent of Carl Sagan. I mean that as the highest compliment that I may offer.
This is the reason why so many people hate math, physics, or anything STEM. They get to a point where they don't understand something and all they get is a book that skips details and doesn't explain well or a teacher who speaks in abstract terms and no longer knows what it's like to be a beginner. It's almost like the world of STEM is an exclusive club, and beginners ain't in it.
Physics is hard because sometimes because of following reasons. 1 I for example don't have background in topology or conformal geometry, so if you start writing such equations in string theory I won't know where to look , which book to learn from . So it would be nice to put an appendix and explain all equations used say of conformal geometry. Another example if you start talking about so3 groups or Su groups I won't understand what these mean. So I suggest make it more transparent. Make a 600 page book rather than a 250 page book. This is why Physics made hard actually it is almost high school if you know the mathematical steps. The real hard part is application. Sometimes I read a chapter in Quantum Mechanic's say entanglement I ask what are the real implications of it. Now being an Engineer by profession I see entanglement as a very powerful thing. But you guys are caught in ideas like superposition states. So for example what is entanglement say in a black hole. Does entanglement contradict Uncertainty. You know you guys are killing oeoples interest in a subject. Reminds me of a Professor teaching me flow around a cylinder. He never mentioned what it really meant, I only realized after I worked on unsteady flow problems around external fuel tanks for large commercial planes at Boeing. Please I suggest to all of you smart people out there, dont cloud the subject, clear the subject. I for one wanted to develop higher than light speed travel. But I get burnt out reading all the math and still feel it raised more questions than answers. Physics has become very muddy to me. Yes I am not that educated perhaps.
In my youth I attempted all sciences at GCSE O'Levels: Bio, Chem, Physics, Math & Add Math. Ended up with Grades 2,2,3,1& 1 respectively. Physics was indeed the hardest of the lot, primarily because so much of it was Applied Math. IMO...unless one has good analytical faculties & an ability to sift relevant information out of such type questions, there's gonna be difficulties later if the subject is pursued further. I eventually opted for Pure Math, Stats & a Biochem minor, when I realized I was more geared toward 'theory' over 'application.' However, I still love some of the more esoteric disciplines like Relativity, Quantum Theory, Astrophysics & Nuclear Physics equally as my joy of higher Math (ongoing Masters level)....🤔
Physics is hard because it is: 1.) for people with the mindset for the subject, 2.) it requires a long attention span, 3.) it requires passion for the subject, 4.) lots of formulas, 5.) terminology, 6.) lots of scary shit, 7.) history lessons, 8.) it requires devotion/loyalty to the subject, 9.) for alternative people (I know from experience), 10.) vocabulary. I'm sure there are several more reasons that I can add to that list.
@@zeus-yz6gs I'm in a good mood, so let me add this: 1.) It's mental...all in the mind. 2.) For me personally, I was somehow fixated on finding a gf/wife. When I told them my interests, only the ones that liked both physics and...Lacuna Coil, were interested in me. 3.) Love interests ruin everything. I would love to go back to a time, when I could be like, what I like, without a graveyard love interest. 4.) I don't understand some people, especially the "darkly inclined." I am sure we can enjoy and love science, without all the unnecessary, Halloween elements.
@@FaCiSmFTW Goth/Alternative. You try to enjoy something, then these trolls ruin it with all kinds of Halloween shit. This is why we can't have nice things.
I'm not here for attention cravers like them. I'm here to learn and enjoy the subject matter. The minute I see something that reminds me of sci-fi bullshit, I want to crush it.
Good advice about practicing algebra. If you're not competent with algebra don't expect to pass physics. Also read the textbook and do the homework. That really helps.
The bit about lack of memorization isn't even that big of a deal, if we're being honest. Plenty of subjects have a heavy factual load (chem, bio, law, politics), but require lots of problem-solving, analytical, abstract thinking, or lateral thinking skills. Memorization and "hard" aren't mutually exclusive. As a Phys major myself, I've always respected those other fields for that reason.
Technically true, but in my experience the more memorization a subject has, the less critical thinking it requires. And critical thinking is significantly more impressive and useful.
As a wee little JEE student, him saying we have nothing to memorize hurt like hell. I'm crying over my stack of bland boring formulae that sucked all the joy and beauty out of this subject that I once loved
@@blue-cs3fk yep. And since we only have two years, we can't go on feeling the essence and joy of physics, since we just have to understand, solve questions and get that chapter done. It's sad...
I’d like to see an answer explaining why mathematics is so hard. I’m a mathematics major myself, though mathematics at uni isn’t so much about calculation as it is about reasoning (proofs).
Physics is definitely not impossible without Calculus knowledge. Calculus definitely adds more context in how you get the formulas for the calculations but my high school physics class was pretty much all algebra based. What also trips a lot of people up is dealing with frames of reference. People get tripped up when it comes to how you establish your coordinates but it really doesn’t matter as long as you are consistent. If you say that (in the case of the x-y plane) that x is positive if moving to the right and y is positive going up you could totally change it if you want as long as you apply that to everything else in the system. This also applies to things like conservation of force and momentum where a force can be considered positive if it’s acting in one direction and another can be negative if it’s acting in the opposite direction. Those concepts always seemed to trip people up who were just taking introductory physics courses. Conceptually physics is not that hard even if you’re not great at math. If you’re not strong in math you will have a hard time with the calculations but the ideas like Newtons laws are not hard to understand.
I do really well in mathematics. It's the application to real world scenarios that I don't click with. However, I heard college physics does less real world application stuff and more mathematical theory stuff.
I was top in my school for Math and Physics, which I loved, for the grade 10 national exams. But I ended up not taking any Physics in University because apparently I needed Chemistry to become an Engineer, and I also didn't want to go the pure academics route, so I ended up doing Math and Finance. Biggest regret I'll ever have in my life, still feeling it 10+ years later.
I had a very satisfying career in experimental physics without having to use much math. That's something the theorists had done for me. All I had to do was to take that math and convert it into machines. :-)
i think theoretical physics is another level of math 🥲 but in general, physics is acceptable if you can commit to it. i was doing pure physics during undergrad, at first i thought i will be the worst but turns out I did better than expected. so don’t worry don’t get scared of math 😆
Nonsense. Several "pure mathematicians" have problems learning Quantum Field Theory because of the PHYSICS and the thorny, conceptual paradoxes that don't always avail themselves to the kind of mathematical intuition "pure mathematicians" tend to have. So, yes, physics is hard because of math, but math isn't FUNDAMENTALLY HARDER than Physics. If you're smart enough to REALLY understand physics, you should understand what I'm saying. I find "pure maths" easier than physics because physics has several constraints - it has to apply to the real world. In math you can draft theorems and lovely conjectures for days; in physics, experiment is king and the marriage between spatial reasoning, numerical reasoning, and verbal reasoning intersects. I'd argue there was greater progress in "pure mathematics" from 1667 to 1867 than there was in physics. If mathematics is fundamentally "harder" that should not have been the case.
@@feynmanschwingere_mc2270 Well said. It's not quite fair to pick that period, of course. The enormous progress in experimental physics in the 20th century was mostly thanks to the development of electrical engineering and modern chemistry/material science, not to mention the trillion dollars that the world invested in nuclear weapons. That paid for a lot of our "toys". What follows is that math is a lot cheaper. Paper and pencil and whiteboards are not that expensive. :-)
@@schmetterling4477 Well said! Until your comment, it hadn't occurred to me that without seminal advances in, effectively, engineering and material sciences, we wouldn't have the experimental leaps (lhc and the Higgs boson - the boson first predicted by Einstein in the 20s) we've seen. I do think that theory tends to be more intellectually challenging. I'm torn on nuclear physics because we now have the capacity to end anthropic life as a know it. Was it worth it? I think not but I'm open to having my mind changed. Scientific progress is hardly ever linear.
I agree with that video but physics have also its concepts so sometimes understanding the concept is difficult more than using an equation to find an answer.
Prof. Hafner, of all the playlist in your channel, please advise which one to start first for the person who did her physics 33 years ago (and still have grudge on her physics teacher)? 😂
I find that mastery of trig is the most difficult aspect personally. Followed by ability to conceptualize. Plenty of people can do the math, but get direction/sign wrong because they can’t see the whole picture.
Yes, that can be a hurdle. But once you get good at figuring out vector components, and then get good at finding right triangles in problems, the trig isn’t too bad.
Physics are an important part of my hobby or slinging. Math is as important for accurate slinging, especially geometry. My sling rotates a lot, so there's centripetal force and trigonometry involved. Don't forget kinetic energy!
Do what you love Just reverse this quote So love what you do Which means you should love and enjoy learning physics... Curiosity is the thing that keeps you learning... ❤️
Great video. The reason certain subjects like this are hard is because of the amount/level of abstraction required. That is why arithmetic is harder than counting (a symbol is more abstract than the real thing). Algebra is harder than arithmetic (variables are more abstract than concrete numbers). Calculus is harder than algebra (introducing the dx is another level of change). And now physics takes the real world into the already abstract world of mathematics. The more levels of abstraction, the greater the percentage of the population that will struggle to understand.
True, but I'd add that physics (intro mechanics) is a chance for students to take that abstraction and apply their physical intuition. It might not provide much relief but maybe helps.. Of course then they get to E&M where they have no intuition!
@@Prof-Hafner I agree! Not sure why I studied electrical engineering. Talk about abstract. But I did love those ah-ha moments in mechanics where everything came together in an experiment and I adjusted my viewpoint so that my intuition started working.
There's a lot of things you can do in physics without hard math, actually. A lot of it is "thing thing is proportional to the square of that thing" and such, and the study of these associations can be understanding-based, not maths-based. And also, a lot of physics is phenomenological. You can certainly approach things like the Heisenberg Uncertainty Principle or the Maxwell Equations through maths, but that will not help these make any sense, unless someone actually cares to explain what the maths really corresponds to.
It's my final year of high school, and physics is one of the subjects im aiming for. My physics teacher did say calculus is crucial, but as we are already familiar with calculus wide and deep, hes still confused about why we cant do simple calculations in physics compared to math.
As a highschool physics teacher, yes the algebra is a barrier. Even though the kids have completed HS Algebra 1 and 2, their math skills are behind where they need to be. Particularly since they don't know how to manipulate literal equations.
It is hard (often) to efficiently and accurately rearrange and solve equations and inequalities. I suppose that if you have software like Mathematica, it helps oodles. And that is more a math issue than a strictly physics modeling issue.
Physics is hard when your physics teacher ignores you!
😭😭😭
physics easy. its our thoughts are the ones making us weak
It's also hard when you're looking for a gf or wife, and all that flocks to you are "the darkly inclined." Some women ruin everything (just the "pretty" goth ones). It shouldn't be about complete and total fiction (i.e. Frankenstein, mad scientists). It should be about the real world. I am SLOWLY getting back my interests, thanks to a co-worker, and my brother.
This is probably true my teacher don't care about us students
@@the11thken That's another reason. In order to make any subject learnable, you need a teacher that cares about students. Not one that loves to be dictator (yells, writes anyone up), not monotonous, and not scary.
What I've been all along is: it's not the subject itself, it's the people. That's true for anything. I love chemistry, biology, and physics. It's the instructors, teachers, classmates, peers, etc. that make or break interest.
Back in 2018 I stopped everything I was doing and just sat down to study and master basic arithmetic and algebra for months. Saved my life. Before I had trouble converting between say decimals and percentages, or dealing with some more involved equations with lots of fractions, powers, and so on. Had trouble with graphing too. I just practiced everything as much as I can, mixing the different skills, testing every scenario, using tools like desmos and geogebra to help me experiment with the concepts. Eventually this made algebra a trivially easy thing to do. Best thing I've done in my life tbh, since a lot of my interests are math based.
I have seen many students who did not care. What made you care enough to really apply yourself?
@@albirtarsha5370 my main motivation is that my interest are really math heavy (astrophysics and machine learning), I told myself if I keep struggling with fractions I won't be able to deal with physics any time soon 😅 so I had to conquer it. If you're a physics teacher you can remind your students of their goals, even if the goal is just to graduate with high grades, and especially if their pursuits involve math, remind them it's always worth it to master the fundamentals, it's a one-and-done thing that will always serve you, better to struggle with just the physics concepts than to struggle with both the physics AND the algebra right? That was my logic 😅
But unfortunately I only did this as an adult after leaving school. During school I just didn't have the time to do this even tho I had the interest, I collected my math textbooks since like 5th grade and always had the plan to set down and really put together everything I have studied and master everything. But unfortunately I just never found the time as a student in K-12. And now since I can't afford higher education I just continue teaching myself my favourite subjects with plenty of time to invest in them.
I want to do the same , what should I do please.?
@miryasin7930 ALEKS online is a good platform for learning math. It is adaptive, so it only makes you do enough problems to learn each lesson. The cost is $20/month, which is cheaper than paying for a tutor.
Can you recommend any resources besides geogabra?
I know Calculus well but for me it's harder to get to the maths part than actually do the maths. So understanding the problem and applying physics to it is where I struggle the most.
that’s exactly the hardest thing about physics. the math (most of the time) isn’t the obstacle
A thermometer has a measurement system.
Before there was one, there wasn’t one.
Physics is like trying to tell a temperature with out the measurement system on the thermometer.
Every new physics calculation is adding another measurement system akin to the one you can find on a thermometer or a ruler; or a calculation that brings math into proportion with a previously known measurement system.
Wave function is one, spin quantum number is one, E=MC2 is one, Cm & Meters is one.
Yada yada.
Once you understand what they mean and where they apply in terms of scale you understand the system.
You do not need maths to do this.
You need maths to discover/prove it but it doesn’t mean to say you need maths to go in the direction of discovering something new.
For example, I don’t understand the maths behind thermodynamics but I understand thermodynamics enough to help not crack my windscreen when it’s frosted over.
I can use this as an analogy to describe phenomena at a molecular level but it doesn’t mean to say I could write it down in an equation.
I think we have the same problem. 😂
@Kaldunaa - What do you think limits your understanding of the problems?
This is normal and it doesn't have to do with your understanding in physics. You're solving a problem, and THAT is the hard part. Even if your understanding of physics is really good and you have a great knowledge of math, it can still be really hard to solve problems that you have never encountered before. Just remember, that even the easiest problems in math, took many years to be solved even by great Mathematicians! And how can you become better at solving problems? Just by practicing and seeing as many solved problems as you can, it's the only way!
Sometimes it's the math, sometimes it's the physics. People sometimes get caught up in the whole idea that physics is physics and not math, that they end up using poor and oversimplified mathematical models for situations that require more sophistication. Spherical cows is a common physics joke. That's where you have to give engineers respect, because they are actually the ones to do detailed fluid and finite element simulations using programs like COMSOL or ANSYS to really analyze the details. Why physicists don't do this is beyond me. It's the same way it is baffling that chemists aren't the ones studying elementary particles but rather physicists are.
When your basics are not clear,then surely it is hard.
i was never taught the basics
what are the basic topics for understanding physics
Ask GPT@@manonmission4827
Please repy
The basics is exactly what's in the video, algebra. Just get really good at manipulating equations, everything will make much more sense if you can follow the derivations. You might also start learning polar form vs Cartesian form, how to convert between the two (that's basically vectors). Knowing integrals is useful for understanding derivative, essential if taking a highly rigorous physics course (major specific intro and above). But yeah, basics=algebra
My secret? after getting an 'F' in upper division Mechanics, I got a student job tutoring physics. I really had to rework my understanding into simple and consistent explanations. I got more out of it than those I was teaching. Coolest thing: The guy who was struggling, but actually kept showing up, and got better and better. He never tried to "just get the answer". Good Times!
Never Quit. Find the most do-able way to "not give up" and succeed. You'll won't regret success.
Thanks for the encouragement bruv
Thanks I need this, about to take physics 2 and I am already wanting to quit after seen final exam is 50% of the grade 😭😭😭😭😭.
@@Nebula2024 I pray you get an A1. Amen.
Physics is hard because it takes experience and practice to learn everything. You can’t simply walk in and be really good at it, you need a good teacher. The issue is way too many physics teachers either won’t give you the time of day, or they are just so busy they can’t give everyone enough time.
My physics teacher admitted she was in the wrong career and then blocked me
Exactly, the teachers must be creative cause there's lots of abstract concepts in physics. Students cannot just sit in the class and imagine everything.
I tried to memorize patterns of procedures of solving physics problems when I was undergrad and eventually realized that it's impossible and you had to be flexible with Maths. Then through a few years I began to see more abstract patterns that I often encounter and I finally noticed IT IS NOTHING BUT ALGEBRA that deal with patterns. Now I'm preparing for phd deffence. Wish I noticed a bit earlier.☠️💀
Interesting way to put it ! All the best with your defense.
@@Jhonnydonny Thank you so much 😭
u got this@@tomofthedepths1742
Can you please elaborate on what you mean by 'it is nothing but algebra that deal with patterns'?
In the context of undergraduate courses in maths, physics and engineering.
So you are saying you grinded math and then became good at physics? What’s the moral here?
Hi, thank you for this analysis. Physics is hard for many students not only because of gaps in their knowledge in maths or because of lack of practice, but also and probably mostly because developing a clear and proper representation (or mental picture) of the problem at hand is not as easy at it seems. As a teacher of physics, I see that a rather large proportion of students in a cohort find it difficult to develop their reasoning. Proper reasoning requires a good knowledge of the notions discussed during the lecture but also an ability to picture mentally the studied problem. This is particularly true for thermodynamics when a key step for problem solving is establishing the correct energy balance.
Yep, there are lots of reasons physics is hard! Visualizing in 3D can also be tricky (related to your point). I am bad at that. I can do it, but I have to really stop and take a minute.
This might explain why I’m excellent at maths but terrible at physics
@@emar22111 Same for me! Though I wanted to become a physicist, I always was better at mathematics. I started uni in a maths program, always keeping in mind a transfer to a physics program at some point, which I did in third year as I felt more confident that I could at least manage the formalism of quantum mechanics, kinetic theory, mechanics, etc. However, it proved extremely difficult for me to adapt to the physics curriculum: the way they do maths in physics is not rigorous and I got frustrated, and my vision of physical systems was always blurred. It took me years, up to PhD level, to adapt and change my habits to become a physicist. Still, I find it easier to teach the mathematical formalism than to teach how to mentally picture physical systems and processes; cognition is something quite personal and there is no recipe that works for all.
You are not the only one. In maths you manipulate symbols. In physics symbols have meaning and it is not an easy task to work with symbols having physical meaning. @@emar22111
UEC physics is nightmare. it is grade 10-12 physics.
As an ex-physics professor I know the answer to this question. I’d like to say my college teaching experience is why I know the answer, but honestly my years of helping and attempting to help my “pre-med” or “other” friends and acquaintances deal with their first physics and calculus courses already taught me where the essence of the difficulty lies for some people. The answer is that Physics, and also Calculus, are very often the first place where a whole LOT of students come up hard against the requirement to turn actual understanding and first principles, rather than rote memorization, into practice. It is the first place in our present educational pathways that many students come up against the a brick wall that is very hard to penetrate with rote learning.
Yes, students are exposed to baby versions of this kind of “thinking on your feet” much earlier, like proving theorems in geometry. And they can fake their way though an imitation of the process in algebra and pre-calculus by memorizing and implementing a small set of rules which they are then taught to apply by rote. But the rubber really hits the road in Physics, Calculus, and especially in the required pre-med “Physics with Calculus” - the horror, the horror!
For many students the memorization-heavy, analytical-thinking-minimal method they have used with great success up to then fails at this crucial juncture. “Fails” is perhaps too strong a word since absolute failure would probably have been a gift at this point. In reality it is more cruel that that - the memorization it takes to avoid fundamental understanding, the FAR easier alternative, ramps up exponentially until it reaches an absurd level forcing a crisis in people that haven’t yet had to face such things previously. An (over) simple example - the absurdity of trying to memorize the “formulas” (x = g(t), v = h(t) ) for every trivial mechanical question involving Newton’s laws rather than learning how to apply them ab initio. Anyway, many of the students that are freaking out at this point are experiencing the failure not of their intelligence, but their highly developed, and by this point time-tested and proven memorization-heavy “learning” (and it is not an exaggeration to call this UNDERSTANDING) techniques.
This problem is something very hard - leaving aside that teaching students HOW to think is not really in the job description - for the professor to simply “teach” the student out of. I know from experience the disconnect when a student that wants “help” but is only prepared to accept it in the form of an answer to “tell me which formula I should memorize?” The frameworks for exchange of information themselves are mismatches - or aptly, “the matrix is something one cannot simply be told about, you have to experience it for yourself”. 😂
For a few or the students, the ones that are already prepared, this is a point they experience as a kind of liberation. For the others, especially some of the pre-meds that are “forced” to endure this trial - coming in to the class with an “I’m gonna hate this, but I have to pass and hopefully get an “A” to get into med school” really doesn’t help - it can seem like nothing makes sense anymore. To have this occur at a time when nearly all of these students are also experiencing a new environment, and new social pressures, well that is a recipe for trouble!
This is a better answer than the video itself
In my junior year of Chemical Engineering I tutored a older nursing student in organic chemistry including some reactions. She was going into nursing from a clinical psych background. When she was able to visualize in 3D and notice things like where a slight charge would be she finally turned the corner. She no longer needed the models. She finally understood why there was more than one product of a reaction and what the probable ratios were. That slight charge thing, that was a tough one to get her to. She understood an electron has a charge, and that is the unit of charge, so how can a compound be slightly charged at different places. It was a victory for both of us and one of my greatest achievements.
When you deal with problems in physics, you have to make sense of the problem and apply concepts to a solution in mathematical terms. You have to build the argument from scratch. This is by far the most challenging part.
This is such a good comment
I'm screenshotting this
But don't students get a lot of that in word problems? That's where they take real (if rather contrived) world problems and apply what they just learned.
I think it comes down to learning preference. In high school, typically the people who take biology (lots of memorising) don't take physics (very conceptual and math heavy), and vice versa. Chemistry is the "middle ground" (both memorising and conceptual, with mostly arithmetic math, and basic algebra) where both physics and biology students take them. If choice is available, students who take all three of those sciences, or those who take physics and biology, are unicorns.
Agree completely. I took biology and physics at the same time, which is what drove me to physics.
I'm literally doing that right now in high school with AP Bio and AP physics. I prefer physics about 100 times more
@@Prof-Hafner
Good luck with those! @@marielaforestsnyder1857
@@marielaforestsnyder1857 same but im taking ap chemistry and ap physics
Chemistry ? Nobody wanted to be my Lab Partner. After a few classes and a "Jaws themed 'ear-worm' infestation", I realized I was surrounded by Pre-Med students who (by the Junior Year) knew each other. The Kiss of Death was "Grading on a Curve". I realized I was the likely to become Chum for the Pre-Meds.
I dropped it in favor of 'Fencing'. From frowns to smiles! Best-Decision-Ever.
I've always dreaded algebra when I first learn it, but now I believe those hard work finally paid off...
Good! :)
what does dread something mean?
@@thiagogregory1 fear, or worry about it
but i know algebra......
I still remember when the lightbulb came on in a physics class in engineering school, as some problem involving a cone and an integral was being considered. It was like "calculus can be tied to a physical problem." It was the first time we used calculus outside a math class. I agree with you - tying it to the real world can make it easier for those not as good at the seemingly abstract mathematical theory alone.
I've always been pretty good at math. When I took relativistic physics I got a reality check on how theoretical I was capable of thinking. Just meet with your physics prof during office hours and send some emails back and forth. The more he/she sees you are trying the more likely (he) will be to help you understand the concepts that he will be testing you on directly. I failed the first test (30% of our grade) and panicked but utilized every office hour session available to study directly with my prof. I ended up acing the midterm (30% of our grade) and think I got a B+ on the final (40% of grade). Ended up passing the class even though I wasn't happy with my overall grade. Still my most memorable class ever with the only one even coming close being differential equations.
Good advice!
It's a good advice and that's also how I got a good grade in calculus.
But you have to have a teacher who's willing to be patient and my current physics teacher is anything but...
im good at maths what happened
Everyday, I'm amazed again and again at the care and dedication you put out in your lectures.
Sir, you are probably the most brilliant and enthusiastic physics teachers in the world.
Hey! Great video dude! Well done! I enjoy hearing your analysis! ❤
Kind sir, thank you. Thank you for sharing this with us.
knowing those little short cuts is helpful like knowing that anything in a denominator on one side can simply be moved to the other side as a numerator so 1/2 on one side can by moved to the other side as 2, 1/x on one side gets moved to the other side as X, etc.
Yeah you want to have all that at your fingertips. So you can focus on the physics
Great video and as an engineer and psychologist, I agree with everything Hafner said. Going deeper however, to be successful in any rigorous academic pursuit, developing critical thinking skills are an absolute necessity. It’s the basis for all logic and math. Developing CT skills takes a LOT of effort and time and does not come naturally to most of us. We tend to believe we are more rational than we really are, so our expectations that maths should be easier to learn than they actually are are usually wrong.
Yes, for sure. This video was made as an intro for a freshman mechanics class, so it is somewhat out of context here on YT. As students move on from freshman classes, there are new challenges like CT and many others! ;)
Yup! I also think that approximations trip up students sometimes. Trained physicists have a good eye for the essential features of a problem and can drop some of the details to approximate. Students can sometimes find all the information overwhelming and not know where to start.
They don't learn approximations in high school. In some cases such as the small-angle approximation in the motion of a pendulum, it is the approximation that makes it possible to solve. I would make the students put their calculators in radian mode, and then have them calculate the sine of .001, .01, and .1. The real logic or the small angle approximation comes from the Taylor-series expansion, but a simple practical demonstration is probably more helpful.
Tried to help, future physicists, good man, good teacher, good work
I teach both physics and calculus and I agree with you 100%. Math is so important. However, I had students who had all A's in math, but did not do well in physics. They just couldn't grasp certain concepts. I think the reason is that in physics no two problems are the same, you can't just memorize some steps on how to solve a problem. In math, including calculus, many procedures, like the product rule, can be memorized without even knowing the proof of the formula using limits. In physics, you can't just memorize that the net force is mass times acceleration. For a simple example, like the Atwood machine, students need to be able to draw a free body diagram and to add all the forces and then solve for acceleration by using algebraic methods like substitution or elimination. That requires a skill and critical thinking.
I taught Engineering Mechanics to first year Engineering students, and that's like physics on steroids. An elementary issue of course is understanding vectors and how to do calculations with them. Another issue, which is why engineers emphasize Free Body Diagrams is understanding the point of application of the force. I find that it can be difficult to convince students that they need to use vectors, but it's even harder to convince them that the point of application of the force is important. It's all kind of detail-based and pedantic, and people don't embrace that. They want it to be easy.
Agreed. There is too much focus on algorithms vs. deep, conceptual learning.
Exactly this! I found math in school easy bc all i had to do was memorise the steps and put it into a calculator but i struggle with physics a lot more because you actually have to understand what your doing to be able to answer a lot of the questions
@@martymcfly1776hey , can you give me any tips how to get good at physics.. please
I love u so much professor.I missed meeting u earlier.Who cares I'm grateful I found u atleast now.Hope to surprise u one day
Oh you're my teacher on edX! So glad I stumbled across this youtube channel
Amen to that. I didn't get far into calculus before realizing that a solid command of algebra was necessary first.
It's translating a word problem into the correct mathematics.
How can I train How can I train this?
One of the problems is that some of the things and connections that can be memorized, abstractized, related to similar concepts or "simplified" in terms of idea, start only after you are already very good at math 😅😅
So, before you reach that level, it's often already "too late", as some people never reach it, already graduated or go for PhD+, which is vast minority 😂
It really takes time and effort to not only get much of skill and knowledge, but also "mathematical intuitions" in certain types of tasks, so you can easily do "educated guesses" etc.
It's really good that physics helps create this intuition!
I remember how our mathematics teacher in secondary school led us to a situation where I felt the need for differential and integral calculus. When I started to study electrical engineering, the calculus already made obvious sense and was something natural but this time in a technical rather than a theoretical-abstract context.
V helpfull for me . Knowledge & education is beautiful. 🙏
For me it wasn’t the math. When I got to upper level physics, it was setting up the problems. I’d either miss key info or neglect a key piece of physics involved in setting up the equations
The best way to learn physics is to have 1000 questions from the simplest, gradually getting more difficult. Memorise your formula for each topic. Practice writing out or telling someone else your understanding of the concepts of each topic. My physics professor always had the whole blackboard full of questions and our lesson was doing each one and he would also talk about the concepts as we went. I remember after attending my first lecture with him, I was so excited to go home and do the assignment for the week. Who gets excited about physics?
Yeah sometimes I worry we go straight to the "deep understanding" problems, when some folks need to start by doing routine problems to get used to the formulas and concepts.
Great explanation.
I was a lost cause at math. The deputy headmaster (Ernie Enderby) gave up his lunch hour to educate me one on one, with no distractions. X & Y meant nothing to me, so Mr Enderby brought in a bag of apples and oranges and used those in place of X & Y so that I could follow, see and visualize the equation.
I failed the exam. I did sit a retake six months later, I passed with the lowest grade. Other subjects I passed easily never gave me the happiness of my math pass, it still pleases me to this day.
I should have gone back to the school to thank Ernie Enderby but I was still young in1973 and had my head up my arse. Thank you Ernie Enderby for giving me your time and effort.
It's wonderful to hear that Mr. Enderby went the extra mile to help you understand math and that you eventually passed the exam. Teachers who dedicate their time and effort to support their students can have a lasting impact on their lives. While it's never too late to express gratitude, it's understandable that you were young and didn't think about it at the time. Nevertheless, it's great that you still appreciate his efforts and the positive effect it had on you. Teachers like Mr. Enderby deserve recognition for their dedication and commitment to their students' success.
Yeah,I've also have difficulty in math,I'm dyslexic and have add. So,I always hated math, however one tutor, Mrs Smith,now a principal was so patient with me,sometimes,I even liked math,learning from her. :)
However, another math teacher,was so shocked at my wrong answer,he cursed at me,in front of the entire class. So,in that class,I never asked for help again.
I actually came here to understand my boyfriend, who is always talking about physics. So, it's not like he's speaking in foreign language he's speaking to me anymore. 🤪
This is subject very dear to my heart .... at 85. I struggled, came close to failing sooo many math classes while a youngster in jr. and high schools. THEN I all but accidentally was taken under the wings of a superb collegiate professional level math professor ... WHO KNEW HOW TO TEACH MATHEMATICS.!!! Within TWO months ... with totally focused, dedicated teaching, he moved me from the basics ... to third order integrals!!!! The man was like magic. Unfortunately, due to other circumstances I was not able to progress into the professional worlds of science, as I so dearly wished to do. However, the event, PROVED so clearly, that the quality of teaching, and instruction, and the overall approach to learning advanced math, is EVERYTHING! (Assuming of course, the student has the 'raw materials' and an eager attitude to start with!) Aside from the qualifications of the instructor, perhaps too, the surrounding atmosphere and sense of importance is also crucial to a successful life in mathmatics and high level science. Inept, or truly unqualified instruction in math ... is a guaranteed path to failure.
It's sad you were unable to live your dream. What prevented you?
I failed physics and ended up with a degree in mechanical engineering. The only reason I passed was because the whole class did so bad, the professor curved final grades like crazy.
The more you do something, the better you get at it. Keep getting better at math, keep doing problems, keep pushing yourself to understand and you’ll get it eventually!
wow things worked out for you ! doing mech rn and im pretty sure i chose the wrong major but im too far down to go back now.
The system isn't the greatest. It's good for making connections.. it's required for measuring people's understanding.. I wish I didn't go to uni after highschool and just read books and self reflected instead of 'keeping up with the jones'
Yes, math is right, but the teacher is the key. The inspiration and the examples and how it all connect.
I like physics for its real world applications and how it is so awesome to make us understand the world around us. But I don't enjoy doing calculations that take too much thinking and I cannot manage to like math classes. It's not a horrible time but I am only pushing through it. So I went for chemistry because it also allows me to learn, in a slightly different way, how the world works (which I tend to prefer, too) and generally uses less maths.
Thank you.
Love from India sir❤
I teach electric circuit theory, and it's the same. Wonderful video to share with my students 🎉
For me it was always about finding a way to represent the problem.
The first week of physics was always about converting units from one to another, and it was strange to me why that only happened in physics class.
Later in life, as I challenged myself to do some really complicated programming, I started to appreciate the skill of representing a problem in a way that allows it to be solved.
But that doesn't mean I ever really got good at physics at all.
If you can wake up at 8AM on a Saturday and are willing to work all day, it begins to get _less_ hard. If you can do that again on a Sunday, even better. And if you aren't good at staring at the wall, you will struggle. Coffee, walls, and time are the best way to do physics. Oh, and scratch paper - don't be afraid to write down every single thought you have, every little intuition, every little hunch, or otherwise seemingly meaningless bit of an idea. Coffee, walls, time, and scratch paper. If, however, that's not how you plan on putting bacon on the table, then it's up to you to figure out your own priorities.
P.S. Never show up to a math/physics class tired. Nothing will stick inside your head. Experience taught me just how important this is.
Great advice
I think many in calculus courses still suffer understanding the algebra, and those in algebra have a hard time doing basic math. This is as courses usually just need a C- to really move forward and those exams are always curved where you might only get 3/10 questions correct and yet "pass". So the student is unprepared to deal with calculus-based physics where the teacher is usually unlikely or not fond of teaching you the underlying math.
Sir.. Can you show some ways which we can study and practice physics
This reminds me of our polytechnical first year, electricity being explained using both calculus (magnetism around a conductor) and alternating current circuits solved using complex numbers.
Both weren't yet taught in maths. So we were taught stuff with methods we didn't know yet. Only at the end of the year stuff came together, but by then the derivation was already passed,.
Sounds about right. These days the challenge is we have a class with folks who already know all that mixes with those who are just taking Calc 1.
I love physics and I understand the theory pretty well but its definitely the math that always gets me.
I think students think physics is hard because we wait until 10th or 11th grade to teach them what we'd like them to know when they graduate high school. If we started teaching physics in 6th grade, and taught them some each year, they wouldn't think it was so hard.
We teach kids "English" and "history" each year until they graduate, but we expect them to absorb all of physics in one class in one year.
Our watering down math and science in the early years causes our students to need a huge catch-up phase at the end.
While I agree, I have to say that, at least in the United States, we do teach "Science" classes all throughout Elementary and Middle School. And in High School students are required to take Biology, Chemistry, and Physics so it's hard to have just more pure Physics class requirements.
@@AB-et6nj Well, science classes like Biology, Chemistry and Physics are not required in my state. You have to take one science class to graduate. If you wish to go to college, the other science classes may help you get in and they would likely help you pass their college level classes once you're there.
The science I was taught before 10th grade was hardly worth my time. It was like "science for history majors".
@@eddarby469 Ah that's right, states make their own rules regarding educational policies. It's a shame
I think that math is a more applied science than math and what I mean by that is that you could get quite good at math without understanding it very deeply on the other side it would be hard to be good at physics without a good understanding of the topic. At the same time I think that Physics is hard to teach since it's hard to understand, so you're kind of in this infinite loop, that's why being good at math isn't enough to be good at physics.
Your awesome prof!
Something like 40% of the lecture time in the first year of my physics degree (Imperial College London, 1989) was devoted to equipping us with the mathematical toolbox to handle the remaining 60% of actual physics, to the extent that the lecturers were drawn from the mathematics department. It wasn't just calculus; there was a strong component of linear algebra, but we certainly were hit pretty early on with differential equations, Green's theorems, complex analysis and numerical quadrature methods.
Now I have a bit of downtime I'm finally teaching myself Lie algebras, just out of interest and 30 years after the fact.
For me, pure maths has been something that I struggled to learn, some concepts in physics intrigued me when I was a kid, I think it's time I should start to learn maths again, it's fascinating, I need to know how these things work.
if u venture out to applied math u might find more motivation to learn, although it harder
Pure math is a bit of a brain fuck. Pretty hard to wrap your head around concepts that are so abstract. I've always found applied math to be easier
As an engineering undergrad, I can attest to the fact that the biggest thing college has taught me is the algebra of the matter will lose you the most points. Doesn't matter where.
fricking tied to the real world explanations, that's what most students who don't click at all with algebra and calculus need
Algebra really is the whole of physics, along with the elaborate problems told in a story to set up a problem. I think a lot of people get lost in the story and lose focus of the goal. What are we solving for? Or basically why are we here, why am I reading this problem? Working backwards helped my physics so much
For me its the opposite. Completed all the math classes in undergrad, but the department's lack of teaching made my math worse, all I learned were derivatives, integrals, and how to regurgitate anything past calc 3. in physics now and applying things/connecting dots is extremely difficult because the problems require context and aren't as concerted/braindead. I honestly feel like college made me worse at math aside from learning integrals. Could also be burnout, I'm a working first-gen student making ends meet.
Try finding some older textbooks, from the 90s. I saw some new maths textbooks and found it didn't make any sense. Teaching methods change over time.
bro i relate to u 100%. burnout is fucking dogshit, and i feel the same way college killed my spirits w so many of these subjects i used to love
For me, when getting started with mechanics for AP Physics, I would say the math was not the issue, but rather how to apply the formulas, concepts, etc to a specific problems
Does applying the formulae to solve questions not encompass math? I think you mean algebra and manipulation of formulae were not the problem.
I study maths in University, and we barely even consider plugging numbers into a formulae to be real maths. Real maths is more about understanding concepts than knowing how to manipulate an equation algebraically.
Yes that’s highschool level physics. Real physics relies on differential equations, advanced calculus and linear algebra, not just elementary algebra
@@epicchocolate1866 yeah my comment was a little naïve. I mean I had seen a glimpse of that sort of math in that class (Physics C=calculus-based), but can only imagine how much more interesting it gets
I graduated from high school in the 60's. I was taught in my first year of Algebra to use what is called the transportation method. Some time after that, maybe years, that I learned the properties of Algebra and realized that the transportation was just a "short cut" to the application of properties. I went on after high school to earn an engineering degree from a prestigious university. I now teach upper high school math and Physics and find students are not as proficient because they were taught the application of the properties to solve Algebra equations. This is somewhat frustrating. I believe we should go back to teaching the way it was taught in the 60's.
My elementary and middle school math foundation was never good. I always asked a lot of why? why? why? questions in all my classes, not to be inane or talk for the sake of hearing my own voice, but because I wanted to get to the bedrock of truth.
I was usually told to shut up and ne quiet, and thus I did terrible in math. Actually developed a real fear (not just a dislike) for it based on the hostility of my teachers. They demanded I just listen, memorize, and do the homework but didnt care if i struggled.
I never learned the logic underlying machinery of WHY, say, the quadratic equation worked so I could do examples in class but never the homework.
Algebra is where it falls apart for me and i know i can learn but feel like i need to go WAY back to basic arithmetic so I have underlying understanding to be prepared for algebra
I'm currently doing my masters in mathematics. In order to truly grasp certain proofs and concepts, I've been making use of memorization and high-level learning. My point being that those two have a role to play even in the technical disciplines! Since math is necessarily very detailed, it's easy to get lost. One might have understood every detail of a proof, but done so at the expense of the bigger picture. Recently, I've been trying to approach proofs in a two-fold way. First, I study them at a high level, and try to understand the main ideas. Then, on my second or even third reading, I worry about the details.
Right, I've often wonder if the approach of teaching (and even going through) proof is a good way to teach/learn. Yeah, you learn (hopefully!) how to proof something or derive something from first principles but you may lose the point why something is useful and even forget (by the time you are through) that there is this or that method (don't know the correct English word) that you could apply in this or that case.
In my youth (before computers) complex arithmetic was used to solve certain electrical circuit (AC) problems. I often complained that I've never seen or heard of a complex or imaginary electricity/electron/current so why do I have these in the equations. Took me years to realise that it is (well, today, it was) a handy MATH tool to deal with sinusoidal signals.
@@Axel_Andersen You're not alone! I often take courses, pass them (though certainly not always), only to understand the point of them a number of years later in a completely different context.
Are you working as a teacher by any chance?
@@marcchristianmosot1524I'm not. How come?
@@RedBar3D Ah, I was just curious. Don't worry about it.
4 years of physics olympiad veteran here, yes, algebra is actually something you want to do as efficiently as possible
Physics based calculus arent usually tricky. And even it you get into distribution type of stuffs they aren't as hard as those you see in Mit integration bee
Trust me, it gets way more complicated in collegiate physics (let alone grad school).
Most of my professors actually give us integration tables. They don’t care about our ability to integrate, they care about our ability to comprehend, digest, and apply complicated physical concepts. We use math, sure. But an actual education in physics goes WAY beyond that.
I am fascinated by physics as applied to astronomy and have great respect for those who can do the math. And this is from someone who went as high as multi-variable calculus.
Sir, you made a very good point. But, one more thing that I'd like to add, that is, I was extremely good at Math in high school, but I was worst at Mechanics, especially Newton's Laws of Motion. I would always face problem in making Free Body Diagrams, and would always mess up where or how the forces would be acting. For example, cases of systems of pulleys where there are horizontal blocks affecting the motion of a falling block, or cases where a man would be in a self-lifting elevator - they troubled me a lot when I solved in conventional ways. It turns out that, its more about certain basic knowledge of Physics or physics common-sense that students usually lack. Most teachers tell that Physics is totally common sense, but infact its really not "totally" common sense.
Yes, the video could go on for many reasons physics is hard! :) Another one is visualizing, which is related to drawing FBD, especially in 3D.
Great point, I think the moment physics first "clicked" with me was when I understood why mass isn't mentioned in some formulas that we're usually told to memorize. Like aside from understanding how integration of force gives me momentum, it's when equation ma = mg and just doing algebra that I was like "ohhhh so that's where the mass gets cancelled out before i go down to finding position and velocity, THIS is why acceleration is the same regardless of weight", something I was always told in highschool but never understood
One of my math professors once said that mathematicians don't always care about applications, and I have always found that mindset quite interesting - it seems strange that someone would devote lots of time on something without caring about why it is useful, but I guess that mathematicians generally view math as a prepared "toolbox" for whatever stuff that people might need.
Mathematics has an inherent beauty. And beauty delights people.
@@lauterunvollkommenheit4344 The beauty is that math is a pure science that appeals to an analytical mind.
@@bobs182 Mathematics is not science. It has its own universe which is independent of the physical one.
Mathematics has been described as a kind of philosophy, and it certainly can be at times.
@@lauterunvollkommenheit4344 I knew when I called math science there was a problem as it would be better described as the language of science. The world functions without humans counting and measuring it.
This is the first of your lectures I've seen; I hope that someone, at some point, has mentioned how much your cadence, intonation, and educational intent is reminiscent of Carl Sagan. I mean that as the highest compliment that I may offer.
That is the highest compliment possible!
Physics is linked with mathematics.. and correlated with lesson to lesson
One big reasons are bad teachers
Absolutely
This is the reason why so many people hate math, physics, or anything STEM. They get to a point where they don't understand something and all they get is a book that skips details and doesn't explain well or a teacher who speaks in abstract terms and no longer knows what it's like to be a beginner. It's almost like the world of STEM is an exclusive club, and beginners ain't in it.
Do we call them teachers when they only read off what's just in the book? 😭😭
My high school (year 11) physics teacher was absolutely awful.
And untalented students
Physics is hard because sometimes because of following reasons.
1 I for example don't have background in topology or conformal geometry, so if you start writing such equations in string theory I won't know where to look , which book to learn from . So it would be nice to put an appendix and explain all equations used say of conformal geometry. Another example if you start talking about so3 groups or Su groups I won't understand what these mean.
So I suggest make it more transparent. Make a 600 page book rather than a 250 page book.
This is why Physics made hard actually it is almost high school if you know the mathematical steps.
The real hard part is application. Sometimes I read a chapter in Quantum Mechanic's say entanglement I ask what are the real implications of it. Now being an Engineer by profession I see entanglement as a very powerful thing. But you guys are caught in ideas like superposition states.
So for example what is entanglement say in a black hole. Does entanglement contradict Uncertainty.
You know you guys are killing oeoples interest in a subject. Reminds me of a Professor teaching me flow around a cylinder. He never mentioned what it really meant, I only realized after I worked on unsteady flow problems around external fuel tanks for large commercial planes at Boeing.
Please I suggest to all of you smart people out there, dont cloud the subject, clear the subject.
I for one wanted to develop higher than light speed travel. But I get burnt out reading all the math and still feel it raised more questions than answers. Physics has become very muddy to me. Yes I am not that educated perhaps.
In my youth I attempted all sciences at GCSE O'Levels:
Bio, Chem, Physics, Math & Add Math. Ended up with Grades 2,2,3,1& 1 respectively.
Physics was indeed the hardest of the lot, primarily because so much of it was Applied Math.
IMO...unless one has good analytical faculties & an ability to sift relevant information out of such type questions, there's gonna be difficulties later if the subject is pursued further.
I eventually opted for Pure Math, Stats & a Biochem minor, when I realized I was more geared toward 'theory' over 'application.'
However, I still love some of the more esoteric disciplines like Relativity, Quantum Theory, Astrophysics & Nuclear Physics equally as my joy of higher Math (ongoing Masters level)....🤔
I personally struggle remembering that stuff is connected and that you can do all sorts of things with the different formulas
Physics is hard because it is: 1.) for people with the mindset for the subject, 2.) it requires a long attention span, 3.) it requires passion for the subject, 4.) lots of formulas, 5.) terminology, 6.) lots of scary shit, 7.) history lessons, 8.) it requires devotion/loyalty to the subject, 9.) for alternative people (I know from experience), 10.) vocabulary. I'm sure there are several more reasons that I can add to that list.
its easier than you think XD
@@zeus-yz6gs I'm in a good mood, so let me add this:
1.) It's mental...all in the mind.
2.) For me personally, I was somehow fixated on finding a gf/wife. When I told them my interests, only the ones that liked both physics and...Lacuna Coil, were interested in me.
3.) Love interests ruin everything. I would love to go back to a time, when I could be like, what I like, without a graveyard love interest.
4.) I don't understand some people, especially the "darkly inclined." I am sure we can enjoy and love science, without all the unnecessary, Halloween elements.
@@mrnasty02106darkly inclined people in physics? Can you explain that further?
@@FaCiSmFTW Goth/Alternative. You try to enjoy something, then these trolls ruin it with all kinds of Halloween shit. This is why we can't have nice things.
I'm not here for attention cravers like them. I'm here to learn and enjoy the subject matter. The minute I see something that reminds me of sci-fi bullshit, I want to crush it.
entirely true i hated physics when i coulndt do any math, now i find physics the easiest subject.
Good advice about practicing algebra. If you're not competent with algebra don't expect to pass physics. Also read the textbook and do the homework. That really helps.
The problem with algebra is all of the unknowns.
(Fr though, practicing how math works is the best way to get better at math)
I love mathematical logic and abstract algebra!
The bit about lack of memorization isn't even that big of a deal, if we're being honest. Plenty of subjects have a heavy factual load (chem, bio, law, politics), but require lots of problem-solving, analytical, abstract thinking, or lateral thinking skills. Memorization and "hard" aren't mutually exclusive. As a Phys major myself, I've always respected those other fields for that reason.
Memorisation is for actors and exams. Any technical job will have plenty of resources to find technical info as needed.
Technically true, but in my experience the more memorization a subject has, the less critical thinking it requires. And critical thinking is significantly more impressive and useful.
@@samuelking4723 yes! Which is why people who specialise in learning by rote have poorer intuition and creativity generally.
As a wee little JEE student, him saying we have nothing to memorize hurt like hell. I'm crying over my stack of bland boring formulae that sucked all the joy and beauty out of this subject that I once loved
Dude. Too relatable... I always wanted to be a physicist. But jee kinda ruined the experience!
@@adityathaker2379 Physics just lost that spark it had once you started studying for JEE, didn't it?
@@blue-cs3fk yep. And since we only have two years, we can't go on feeling the essence and joy of physics, since we just have to understand, solve questions and get that chapter done. It's sad...
I’d like to see an answer explaining why mathematics is so hard. I’m a mathematics major myself, though mathematics at uni isn’t so much about calculation as it is about reasoning (proofs).
That's a very honest answer.
Moral of the story: It's not the physics that is hard, it's the maths...
But especially the calculus
Elementary particle physics is further complicated by the fact that it becomes wackier the deeper you get into it.
Physics is hard for most people because it requires common sense and logic. Most people are lacking in those qualities.
No much of physics isn’t common sense, that’s why it’s hard
Physics is definitely not impossible without Calculus knowledge. Calculus definitely adds more context in how you get the formulas for the calculations but my high school physics class was pretty much all algebra based.
What also trips a lot of people up is dealing with frames of reference. People get tripped up when it comes to how you establish your coordinates but it really doesn’t matter as long as you are consistent. If you say that (in the case of the x-y plane) that x is positive if moving to the right and y is positive going up you could totally change it if you want as long as you apply that to everything else in the system. This also applies to things like conservation of force and momentum where a force can be considered positive if it’s acting in one direction and another can be negative if it’s acting in the opposite direction.
Those concepts always seemed to trip people up who were just taking introductory physics courses.
Conceptually physics is not that hard even if you’re not great at math. If you’re not strong in math you will have a hard time with the calculations but the ideas like Newtons laws are not hard to understand.
it's quite simple, it just requires a lot computational power, but music helps me think.
Me who completed my physics exam within 30 minutes:😮💨😮💨😮💨😮💨😮💨
lol
The question is not "why physics is hard"
And the question is not "why math is hard"
But the real question is "why the nature behave like this"
I do really well in mathematics. It's the application to real world scenarios that I don't click with. However, I heard college physics does less real world application stuff and more mathematical theory stuff.
I was top in my school for Math and Physics, which I loved, for the grade 10 national exams. But I ended up not taking any Physics in University because apparently I needed Chemistry to become an Engineer, and I also didn't want to go the pure academics route, so I ended up doing Math and Finance. Biggest regret I'll ever have in my life, still feeling it 10+ years later.
Let's all go back and do physics together in our 40s.
PS, Chem is just math with more labels. Best way to think about it imo
In short physics is hard due to math... And I'm telling you that just think about pure math how difficult and abstract it is !!!
I had a very satisfying career in experimental physics without having to use much math. That's something the theorists had done for me. All I had to do was to take that math and convert it into machines. :-)
i think theoretical physics is another level of math 🥲 but in general, physics is acceptable if you can commit to it. i was doing pure physics during undergrad, at first i thought i will be the worst but turns out I did better than expected. so don’t worry don’t get scared of math 😆
Nonsense. Several "pure mathematicians" have problems learning Quantum Field Theory because of the PHYSICS and the thorny, conceptual paradoxes that don't always avail themselves to the kind of mathematical intuition "pure mathematicians" tend to have.
So, yes, physics is hard because of math, but math isn't FUNDAMENTALLY HARDER than Physics.
If you're smart enough to REALLY understand physics, you should understand what I'm saying.
I find "pure maths" easier than physics because physics has several constraints - it has to apply to the real world. In math you can draft theorems and lovely conjectures for days; in physics, experiment is king and the marriage between spatial reasoning, numerical reasoning, and verbal reasoning intersects.
I'd argue there was greater progress in "pure mathematics" from 1667 to 1867 than there was in physics. If mathematics is fundamentally "harder" that should not have been the case.
@@feynmanschwingere_mc2270 Well said. It's not quite fair to pick that period, of course. The enormous progress in experimental physics in the 20th century was mostly thanks to the development of electrical engineering and modern chemistry/material science, not to mention the trillion dollars that the world invested in nuclear weapons. That paid for a lot of our "toys". What follows is that math is a lot cheaper. Paper and pencil and whiteboards are not that expensive. :-)
@@schmetterling4477 Well said!
Until your comment, it hadn't occurred to me that without seminal advances in, effectively, engineering and material sciences, we wouldn't have the experimental leaps (lhc and the Higgs boson - the boson first predicted by Einstein in the 20s) we've seen. I do think that theory tends to be more intellectually challenging.
I'm torn on nuclear physics because we now have the capacity to end anthropic life as a know it.
Was it worth it? I think not but I'm open to having my mind changed.
Scientific progress is hardly ever linear.
Skill issue
I agree with that video but physics have also its concepts so sometimes understanding the concept is difficult more than using an equation to find an answer.
Cause there's so many laws by stage and by phase of comparison and integration of them is complex
Prof. Hafner, of all the playlist in your channel, please advise which one to start first for the person who did her physics 33 years ago (and still have grudge on her physics teacher)? 😂
This one:
ua-cam.com/play/PL9_sR6QqqcynakTkbhxxnpcgfQC0k3PLE.html&si=D8mU7sSDS-xrk-rZ
I find that mastery of trig is the most difficult aspect personally. Followed by ability to conceptualize. Plenty of people can do the math, but get direction/sign wrong because they can’t see the whole picture.
Yes, that can be a hurdle. But once you get good at figuring out vector components, and then get good at finding right triangles in problems, the trig isn’t too bad.
I wish I had a teacher like you when I was 14
Physics are an important part of my hobby or slinging. Math is as important for accurate slinging, especially geometry.
My sling rotates a lot, so there's centripetal force and trigonometry involved. Don't forget kinetic energy!
Do what you love
Just reverse this quote
So love what you do
Which means you should love and enjoy learning physics...
Curiosity is the thing that keeps you learning... ❤️
Great video. The reason certain subjects like this are hard is because of the amount/level of abstraction required. That is why arithmetic is harder than counting (a symbol is more abstract than the real thing). Algebra is harder than arithmetic (variables are more abstract than concrete numbers). Calculus is harder than algebra (introducing the dx is another level of change). And now physics takes the real world into the already abstract world of mathematics.
The more levels of abstraction, the greater the percentage of the population that will struggle to understand.
True, but I'd add that physics (intro mechanics) is a chance for students to take that abstraction and apply their physical intuition. It might not provide much relief but maybe helps.. Of course then they get to E&M where they have no intuition!
@@Prof-Hafner I agree! Not sure why I studied electrical engineering. Talk about abstract. But I did love those ah-ha moments in mechanics where everything came together in an experiment and I adjusted my viewpoint so that my intuition started working.
There's a lot of things you can do in physics without hard math, actually.
A lot of it is "thing thing is proportional to the square of that thing" and such, and the study of these associations can be understanding-based, not maths-based.
And also, a lot of physics is phenomenological. You can certainly approach things like the Heisenberg Uncertainty Principle or the Maxwell Equations through maths, but that will not help these make any sense, unless someone actually cares to explain what the maths really corresponds to.
It's my final year of high school, and physics is one of the subjects im aiming for. My physics teacher did say calculus is crucial, but as we are already familiar with calculus wide and deep, hes still confused about why we cant do simple calculations in physics compared to math.
OMG! Terrifying. My hat is off to all the physics/math brains in the world.
As a highschool physics teacher, yes the algebra is a barrier. Even though the kids have completed HS Algebra 1 and 2, their math skills are behind where they need to be. Particularly since they don't know how to manipulate literal equations.
It is hard (often) to efficiently and accurately rearrange and solve equations and inequalities. I suppose that if you have software like Mathematica, it helps oodles. And that is more a math issue than a strictly physics modeling issue.
The physics of pointing the camera at an angle where viewers can see something else other than something that everybody else has would great.
If you’re referring to my live lecture videos, they are 180 format. You can drag the screen and look at whatever you want.