the reason for the duel is still not clear. Not "duel for woman", knowing that he'd been in prison before due to political reason, ya know who had to come up all with such claim, akin to falling apple on newton's head 🤣
Yep. I am hoping to finisb a BA or BS in math and Ill be doing all those classes hopefully. Maybe not complex analysis. Depends on what school I transfer to because my online program doesnt have that class online but they may have it on campus.
If a student hasn't yet seen proofs, and is used to breezing through on their intuition, they may find their first core major courses like real analysis and abstract algebra to be quite challenging. That said, don't be scared off from taking math courses! It's just going to take some hard work to get through the material.
Wait, there are people who have math intuition??? Jokes aside, I'm dreading proofs. I'm gonna have to do them eventually as part of my major's math requirements, and I'm the guy who had trouble with algebra of all things
It's set theory but with dozens of slightly different definitions for slightly different concepts and a combinatorial explosion of theorems connecting them all.
@@SevenRiderAirForce That depends on what you mean by set theory. If you mean manipulating sets, moving around element, then sure, some of the theorems in introductory topology are like that. After that, the two subjects general diverge quite a bit. When you are talking about function spaces, completeness, Lebesgue dimension, manifolds, etc. you go quite far away from set theory. Although, there is a lot to say about set theory and topology, such as S and L spaces, Suslin hypothesis, etc. Beyond that, when you get to the realm of algebraic number theory, you have completely left set theory, to my knowledge, there is very little connection there.
@@ethanbottomley-mason8447 Yes, I mean general/point set topology and basic set theory. The amount of ink spilled on that stuff alone is pretty immense. The review of the second edition of Counterexamples in Topology in the Advances in Mathematics journal called it "the updated journal of a continuing expedition to the never-never land of general topology."
We need better teaching at higher levels in math. Usually, the only people knowledge enough to teach these classes are absolutely brilliant and a lot of it comes too easy for them to know how to teach well.
Just finished up real analysis and abstract this year! Both are super challenging. I dropped analysis 1 the first time I took it (last spring). Thankful that I got through the hard stuff! Wishing the best for all future students that take them! Special props for anyone that does any of these courses at the same time. 🤪
Excellent intro to the tough math classes. I was a computer science major so I didn't take all of them but I did take some. I took Abstract Algebra and I really liked it. I had a good teacher. I took two courses in Linear Algebra. The first was the practical, engineering-based one, the second the theoretical proof-based one. That second one was a tough course.
Another "hard" class would be Combinatorial Analysis & Graph Theory. These truly force you to THINK just to totally understand the problem. They have tons of interesting problems and applications
I wanna get my PHD in math but I’m just really nervous to jump straight in. All of these things sound so stressful. I’m so conflicted tbh but I’m gonna go for it
I had an amazing professor for Abstract Algebra which helped me to love that class. I took Real Analysis 1 and 2 which was very challenging but it was interesting to actually prove the concepts we learned in Calculus. Number Theory was very challenging for me. Also, Geometry can be extremely challenging depending on the professor and how far they take it.
Have you encountered any foundation courses? Axiomatic Set Theory, Predicate Calculus, basic Model Theory, Gödel's Incompleteness Theorems, Category Theory? Find it is a bit of an adjustment even for some strong students, if they encounter one of these if all the did before was a basic analysis or algebra (just groups, rings and fields, nothing further like any Representation or Galois Theory) course. Also find students struggle with a rigorous Probability Theory course. What are your perceptions?
The existential proofs in analysis are straight up magic for the uninitiated... And I also found combinatorics hard to grasp because of how unsystematic it is compared to the other more theory heavy subjects.
proof subjects are very hard and abstract algebra, during those times i asked if i take a right course..haha..but my love of math is my inspiration so i pursued... great content sir
Topology agree, but mostly because my lecturer was an asshat, the material was mostly okay. The class on weather dynamics was harder than expected. Advanced topics like c*algebra were brutal. From stats : rigorous probability theory, random matrices, bayesian methods, these were challenging - you could almost sum that up as any subject that proves convergence theorems.
In analysis everything was well defined. Hence clear. Hence easy. Hella easier than my Calculus3. . But I studied topology before I took analysis. That might be partly why. . The assignment grader hated me. I would solve the analysis problems in terms of open coverings, etc,
What's going on here is that the last 2 years are completely different than the first 2 years of math study at University. If you find proof-based courses hard, you will struggle with most of the last two years. Sadly, you won't realize this until you're a junior.
The hardest math class I've done was at the graduate level: measure theory. Analysis was the hardest at the undergraduate level. It sucked, but we worked in general metric spaces so that analysis at the graduate level wasn't so horrifying. Some upper level physics classes will also be challenging for math majors. I remember a class in classical mechanics being challenging.
@@mattbalfe2983 It was indeed in a mechanics class. I remember a lot of computations that that took pages and pages of writing and always seemed to require using some clever trick to compute an integral.
I'm not a math major, I'm a chemistry major, so ALL of the math classes were rough for me. I barely squeaked by everything from algebra to trig, and eventually dropped out of calc 1. The holes in my understanding were like a slice of swiss cheese, so I realized I didn't stand a chance without a full self-studied reset. Needless to say, I'm not off to a great start lol
As a math major, the hardest class I took was point set topology. There was no book, all the answers were in the professors head. Usually if I didn't understand something in class I could always go to the book.
Ye same, Maybe first an easy example to understand what the subject is about and then later why this example can be formulated harder Anyway i wanna see more math ;)
Hi Brian, According to your experience and knowledge, could you kindly advise what are 5 easy/manageable for the list below? Abstract Algebra Advanced Calculus Applied Mathematics Calculus IV (Differential Equations) Complex Variables Cryptography and Cryptanalysis Geometry (prerequisite of calculus or more advanced math) Graph Theory History of Mathematics Mathematical Logic Mathematical Modeling Matrix Algebra Modern Algebra Multivariate Analysis Non-Parametric Statistics Number Theory Projective Geometry Sampling Theory Topology
Abstract algebra and advanced calc. When I got done with advanced calc I said thats it for complex proofs I'm avoiding that shit. Next semester I saw abstract algebra as an elective and was like 'O that should be an easy go' --___-- I will say linear alg can get wicked if you get a professor that believes you should be an expert on it, my exams were 7 pages front and back, ya got an hour and fifteen go.
I wonder how many math majors first thought that abstract algebra was just algebra but more abstract only to find out how gravely mistaken they were looking through an abstract algebra textbook. 😂
"Linear operator groups in Hilbert spaces" was a bit tricky. The hardest course I took was on Ricci flow, a lot of knowledge in algebraic topology, homotopy and homology theory was required.
BEFORE taking any of these classes: Real Analysis, Abstract Algebra, Topology, Complex Analysis be sure you excel at writing proofs and know or can create a lot of counterexamples. Taking just the core Calculus sequence, Computational Linear Algebra and Differential Eqns is insufficient. These advanced classes are totally UNLIKE computational "plug-in"/technique based courses. Taking Logic and Proof Writing classes should help.
classes where maths lecturers uses their own notations without following textbooks, like homology (the topic after galois theory) or complex analysis (if they use rudin instead of ahlfors)
Definetly Algebraic Geometry I is the hardest course I did so far. If you like Algebra and don't want to do much Algebraic geometry, don't worry there is still Representation Theory.
Im taking Real analysis this semester and my braiin literally hurts from all the theorems and proofs....Of all the math I've done nothing beats this class ngl!!!
linear algebra has been one of my favorites so far, my professor did a bit of a hybrid course in that it was mostly computational but there were some proofs, such a fun subject area!
My math degree was very painful but very rewarding hoping to land a job soon 🤞🏼 any tips for what kind of jobs i should be applying for? Got some experience in java,c#,and sql had a theoretical math degree
It can certainly be a challenge depending on which level you take it at and which instructor, though the course tends to be more formulaic (which is nice)
I'm attempting to minor in math and I got to the part of calculus involving series and differential equations. Thought I was doing good but then the exams came around and it was a bad experience. The class was online and the profs didn't give any homework, you were supposed to practice problems until the exams. Not really a fair way to mark things imo.
If you're not doing lots and lots of problems, it would be impossible to succeed. Doing problems to a mathematician is like having training/practice sessions to an athlete. Stephen Curry would be at best an average basketball player if he did not practice at all.
Did I say that practice wasn't valuable? You you what else is valuable? Feedback on your work as you're learning. You don't just cram all your marks into a couple exams.
I should have mentioned too that the exams were online and they didn't offer any opportunity to show your work, you were given multiple choice questions and that was it.
Best part of taking an algebra course was everyone looking at you like you're an idiot taking algebra in junior year. I thought you were a math major? Come on I took that crap in high school lol. So then I'd pull out my copy of Lang and ask for help with a problem.
Just graduated with a math degree (June 2022). This is my list (not in order): Also keep in mind that I didn’t take ALL math classes since some were math electives. Hard: 1) Real Analysis 2) Differential Equations 3) Group Theory Medium: 1) Number Theory 2) Linear Algebra 3) Stats Easy: 1) All Calculus courses 2) Discrete Math Unrelated courses: Hard: 1) Computer Science (c++) (topics I struggled Linear linked lists, external files, and so on) this class was by far the hardest for me Medium: 1) Architecture (was my major before I switched to math. Not very hard but a lot of time is spent) 2) Biology Easy) - All of the general education classes - writing classes Overall as a math graduate, many classes for me were easy and I’m surprised how “easy” it was for me. Never really struggled and it’s interesting how other people see math as hard. It’s all about being consistent. The only class that really gave me a challenge and I didn’t pass, was intro computer science (c++). Which might surprise some people. I was good at math but I guess wasn’t so good with computers. As of now though, I’m confident I could pass if I retook it. Another class for me that was hard but managed to pass was Real Analysis, Group Theory and Differential Equations.
I'm not a math major, but real analysis found a way to ruin my life as well... :D It's kind of interesting, but it's very theoretical IMO, lord knows I can't remember all the proofs...
As a research student i can say Real analysis and abstract algebra sums up the whole universe.... It's just everything around us whether we feel it or not but it is.
What about differential equations and partial differential equations? I found those to be tough since they have a lot of information to cover. All of my proof classes have actually been pretty easy though
Abstract Algebra without a doubt was the most difficult. I have a BA and MA in math. That subject alone discouraged me from pursuing a PhD in math. So I got a PhD in Engineering. My favorite topic was Numerical Analysis. Great way to get around theory. I used it a lot in my engineering career.
🎓Become a Math Master With My Intro To Proofs Course! (FREE ON UA-cam)
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Abstract algebra. Whenever things went past groups my head started to ring. :)
I wish I could double heart this comment.
Pun of the month... very funny :D
We all had a field day with that course.
When it comes to solvable and nilpotent groups, things get more weird in stead of abstract.
Funny joke, but actually Abstract Algebra is the only thing which I really enjoy 😂 (3rd semester Master studies here).
Galois Theory was the most beautiful but challenging course I took in my undergrad. To think a 19 year old frenchman had that in their head.
just to think that such a genius died at such a young age in such a dramatic context makes me sad
he was a simp
@@24spoce8 LOL
@@24spoce8 yes.
the reason for the duel is still not clear. Not "duel for woman", knowing that he'd been in prison before due to political reason, ya know who had to come up all with such claim, akin to falling apple on newton's head 🤣
Real analysis, abstract algebra, topology, complex analysis, linear algebra -- so you're basically saying that the core classes are the hardest?
Seems that's the way it was for me - could be different for you. Thanks for watching!
Yep. I am hoping to finisb a BA or BS in math and Ill be doing all those classes hopefully. Maybe not complex analysis. Depends on what school I transfer to because my online program doesnt have that class online but they may have it on campus.
The hardest course I faced was Ricci Flow. A solid understanding of algebraic topology, especially homotopy and homology theory was required.
If a student hasn't yet seen proofs, and is used to breezing through on their intuition, they may find their first core major courses like real analysis and abstract algebra to be quite challenging. That said, don't be scared off from taking math courses! It's just going to take some hard work to get through the material.
Wait, there are people who have math intuition???
Jokes aside, I'm dreading proofs. I'm gonna have to do them eventually as part of my major's math requirements, and I'm the guy who had trouble with algebra of all things
Logic has definitely been the hardest one I have ever taken. The one about Gödel’s incompleteness theorem.
Can be very tough!!
@@BriTheMathGuy for whimps lol,
@@KAIZORIANEMPIRE Yeah. I bet a genius like you could easily solve it. Anyone who can't is a "whimp".
@@lightningbolt4419 lol
Topology is absolutely insane. I learned about it just recently and the steps taken to answer the question shattered my mind. It seems so cool though.
It's set theory but with dozens of slightly different definitions for slightly different concepts and a combinatorial explosion of theorems connecting them all.
@@SevenRiderAirForce That depends on what you mean by set theory. If you mean manipulating sets, moving around element, then sure, some of the theorems in introductory topology are like that. After that, the two subjects general diverge quite a bit. When you are talking about function spaces, completeness, Lebesgue dimension, manifolds, etc. you go quite far away from set theory. Although, there is a lot to say about set theory and topology, such as S and L spaces, Suslin hypothesis, etc.
Beyond that, when you get to the realm of algebraic number theory, you have completely left set theory, to my knowledge, there is very little connection there.
@@ethanbottomley-mason8447 Yes, I mean general/point set topology and basic set theory. The amount of ink spilled on that stuff alone is pretty immense. The review of the second edition of Counterexamples in Topology in the Advances in Mathematics journal called it "the updated journal of a continuing expedition to the never-never land of general topology."
Calculus is making products in a machine shop.
Analysis is creating the tools.
Nice!
My linear algebra class is supposed to be the computational type, but my prof makes it proof based. I really loved the course.
00:24 - Real analysis and proof
01:56 - abstract algebra
03:20 - general topology
05:29 - linear algebra and complex analysis
Took abstract algebra 1 (mostly groups, rings and fields but not vector spaces) in first year. It was really abstract, but i really loved it.
Wait there’s 2!??
@@Alaska-mk4ok depends on how the school programs it. Some schools take 2 semesters, but mostly just one.
"Mathematics is difficult, even for mathematicians." ~ Reinhold Böhme, quoted in "Vector Calculus" (2nd Edition) by Marsden & Tromba.
We need better teaching at higher levels in math. Usually, the only people knowledge enough to teach these classes are absolutely brilliant and a lot of it comes too easy for them to know how to teach well.
Just finished up real analysis and abstract this year! Both are super challenging. I dropped analysis 1 the first time I took it (last spring). Thankful that I got through the hard stuff! Wishing the best for all future students that take them! Special props for anyone that does any of these courses at the same time. 🤪
Nice work! Very glad to hear you got through it.
Would like to take Real Analysis 1 and Modern Abstract Algebra next semester 🙃
Excellent intro to the tough math classes. I was a computer science major so I didn't take all of them but I did take some. I took Abstract Algebra and I really liked it. I had a good teacher. I took two courses in Linear Algebra. The first was the practical, engineering-based one, the second the theoretical proof-based one. That second one was a tough course.
Another "hard" class would be Combinatorial Analysis & Graph Theory. These truly force you to THINK just to totally understand the problem. They have tons of interesting problems and applications
I wanna get my PHD in math but I’m just really nervous to jump straight in. All of these things sound so stressful. I’m so conflicted tbh but I’m gonna go for it
go for it!
I had an amazing professor for Abstract Algebra which helped me to love that class. I took Real Analysis 1 and 2 which was very challenging but it was interesting to actually prove the concepts we learned in Calculus. Number Theory was very challenging for me. Also, Geometry can be extremely challenging depending on the professor and how far they take it.
Thanks for sharing!
number theory is only for those who've followed up olympiad their whole life
Interpersonal Relationships 😂
Have you encountered any foundation courses? Axiomatic Set Theory, Predicate Calculus, basic Model Theory, Gödel's Incompleteness Theorems, Category Theory? Find it is a bit of an adjustment even for some strong students, if they encounter one of these if all the did before was a basic analysis or algebra (just groups, rings and fields, nothing further like any Representation or Galois Theory) course. Also find students struggle with a rigorous Probability Theory course. What are your perceptions?
The existential proofs in analysis are straight up magic for the uninitiated... And I also found combinatorics hard to grasp because of how unsystematic it is compared to the other more theory heavy subjects.
proof subjects are very hard and abstract algebra, during those times i asked if i take a right course..haha..but my love of math is my inspiration so i pursued... great content sir
Topology agree, but mostly because my lecturer was an asshat, the material was mostly okay. The class on weather dynamics was harder than expected. Advanced topics like c*algebra were brutal.
From stats : rigorous probability theory, random matrices, bayesian methods, these were challenging - you could almost sum that up as any subject that proves convergence theorems.
In analysis everything was well defined. Hence clear. Hence easy. Hella easier than my Calculus3.
.
But I studied topology before I took analysis. That might be partly why.
.
The assignment grader hated me. I would solve the analysis problems in terms of open coverings, etc,
ahahahahha that is way to funny
What's going on here is that the last 2 years are completely different than the first 2 years of math study at University. If you find proof-based courses hard, you will struggle with most of the last two years. Sadly, you won't realize this until you're a junior.
When you have epsilon on either side of you, it's time to leave the neighborhood. :D
ha! Nice :)
Algebraic Topology.
I've already taken real analysis in one variable and ring theory... Topology is coming next semester :)
For me it was measure theory... that was when I really hit a wall and felt that the topic was just on a different level.
The hardest math class I've done was at the graduate level: measure theory. Analysis was the hardest at the undergraduate level. It sucked, but we worked in general metric spaces so that analysis at the graduate level wasn't so horrifying. Some upper level physics classes will also be challenging for math majors. I remember a class in classical mechanics being challenging.
What book did you study undergraduate real analysis from?
@@JB-iu7jq We used "Introductory Real Analysis" by Kolmogorov. Affordable, but not the best for a first course in the subject.
@@Jim-be8sj Definitely! I just looked at a few pages, seems like a hard book to follow.
I'm guessing you were doing lagrangian mechanics?
@@mattbalfe2983 It was indeed in a mechanics class. I remember a lot of computations that that took pages and pages of writing and always seemed to require using some clever trick to compute an integral.
Differential Geometry and Stocastic Process.
Can’t wait to take both abstract algebra and real analysis next semester
Yeah love that advanced linear algebra mention,
A great subject, very challenging at times. Thanks for watching!
I’m taking real analysis right now as a senior and I’m stressing
You can do it!
I'm not a math major, I'm a chemistry major, so ALL of the math classes were rough for me. I barely squeaked by everything from algebra to trig, and eventually dropped out of calc 1. The holes in my understanding were like a slice of swiss cheese, so I realized I didn't stand a chance without a full self-studied reset. Needless to say, I'm not off to a great start lol
Real Analysis is the hardest one for sure
Well.. partial differential equations can also be very hard
As a math major, the hardest class I took was point set topology. There was no book, all the answers were in the professors head. Usually if I didn't understand something in class I could always go to the book.
I think some kind of examples would be amazing!
Ye same,
Maybe first an easy example to understand what the subject is about and then later why this example can be formulated harder
Anyway i wanna see more math ;)
Why does it sound like you haven't done any Modules in Statistics. Because I'd say Regression Analysis is also one
Depending on the course and instructor it certainly can be!
Also partial differential equations was a hard course for me :v
I agree algebraic topology is a pain esp that book spanier. Algebraic geometry was a pain too.
Hi Brian,
According to your experience and knowledge, could you kindly advise what are 5 easy/manageable for the list below?
Abstract Algebra
Advanced Calculus
Applied Mathematics
Calculus IV (Differential Equations)
Complex Variables
Cryptography and Cryptanalysis
Geometry (prerequisite of calculus or more advanced math)
Graph Theory
History of Mathematics
Mathematical Logic
Mathematical Modeling
Matrix Algebra
Modern Algebra
Multivariate Analysis
Non-Parametric Statistics
Number Theory
Projective Geometry
Sampling Theory
Topology
I also struggled in Topology. Nice to know it's not just me
Abstract algebra and advanced calc. When I got done with advanced calc I said thats it for complex proofs I'm avoiding that shit. Next semester I saw abstract algebra as an elective and was like 'O that should be an easy go' --___--
I will say linear alg can get wicked if you get a professor that believes you should be an expert on it, my exams were 7 pages front and back, ya got an hour and fifteen go.
It wasn't the hardest class, but the one I hated the most was complex variables. It was incredibly tedious.
4:26 I could not wrap my head around the concepts( in topology) 😂
Breeze through Calc 1,2,3. Then ... Linear Algebra using Halmos for first rigorous math course. Ya, sure.
I wonder how many math majors first thought that abstract algebra was just algebra but more abstract only to find out how gravely mistaken they were looking through an abstract algebra textbook. 😂
I feel personally called out here. Abstract algebra was too much for me and I vowed to return to it later.
watching this while struggling with college algebra
Real Analysis
Abstract Algebra
Algebraic Topology
algebraic topology, global analysis, axiomatic set theory off the top of my head
"Linear operator groups in Hilbert spaces" was a bit tricky. The hardest course I took was on Ricci flow, a lot of knowledge in algebraic topology, homotopy and homology theory was required.
Yeah and how would you know ?
BEFORE taking any of these classes: Real Analysis, Abstract Algebra, Topology, Complex Analysis be sure you excel at writing proofs and know or can create a lot of counterexamples. Taking just the core Calculus sequence, Computational Linear Algebra and Differential Eqns is insufficient. These advanced classes are totally UNLIKE computational "plug-in"/technique based courses. Taking Logic and Proof Writing classes should help.
classes where maths lecturers uses their own notations without following textbooks, like homology (the topic after galois theory) or complex analysis (if they use rudin instead of ahlfors)
Definetly Algebraic Geometry I is the hardest course I did so far. If you like Algebra and don't want to do much Algebraic geometry, don't worry there is still Representation Theory.
Im taking Real analysis this semester and my braiin literally hurts from all the theorems and proofs....Of all the math I've done nothing beats this class ngl!!!
Linear algebra was the hardest but I really enjoyed it except for the vector space proofs
so week 2 material
nothing is.
Topology is differently the hardest but I thought complex analysis would be number 2 and real being number one. This is how it is at my university.
Yike I'm doing Calc 2, group theory and real analysis all next semester (first year).
If you take a higher level class in Mathematical Logic it gets pretty messed up once you start to study Gödel
Yeah that’s right
@Osmium _ Read Naive Set Theory by Paul Halmos.
@Osmium _ Dover has a good book.
Typo a good book on that
Dishonorable mention: Graph Theory!!
For sure!
so true
do u think an average person can get through a math major?
Topology was pretty intuitive for me but I disliked number theory and propability the most.
Calculus for Business Majors
Brazas' Algebraic Topology was heavy, but it was the most approachable form of the topic.
linear algebra has been one of my favorites so far, my professor did a bit of a hybrid course in that it was mostly computational but there were some proofs, such a fun subject area!
Algebraic topology. My head was spinning so much that I couldn't even tell my a$$ from two holes in the ground.
My math degree was very painful but very rewarding hoping to land a job soon 🤞🏼 any tips for what kind of jobs i should be applying for? Got some experience in java,c#,and sql had a theoretical math degree
Plenty of jobs in data science and machine learning. Try to learn some Python and statistics/probability
abstract-algebra is my nightmare coupled with advanced probability.
listed almost all of them
I'm a double math major sophomore applied maths and maths really scared😭
You can do it!
@@BriTheMathGuy I finished linear algebra for math majors and Physics now for rest of 2020 it's real Analysis and algebra
To me I will never be a math major because statistics and I don’t get along
Definitely Abstract Algebra.
differential geometry
Can a math major get a career in engineering
I definitely think it's possible.
@@BriTheMathGuy Yes it can be done. I have done it myself.
What about calculus based probability and statistics
It can certainly be a challenge depending on which level you take it at and which instructor, though the course tends to be more formulaic (which is nice)
measure theory has been pretty hard tbh
You can do it!
I'm attempting to minor in math and I got to the part of calculus involving series and differential equations. Thought I was doing good but then the exams came around and it was a bad experience. The class was online and the profs didn't give any homework, you were supposed to practice problems until the exams. Not really a fair way to mark things imo.
If you're not doing lots and lots of problems, it would be impossible to succeed. Doing problems to a mathematician is like having training/practice sessions to an athlete. Stephen Curry would be at best an average basketball player if he did not practice at all.
Did I say that practice wasn't valuable? You you what else is valuable? Feedback on your work as you're learning. You don't just cram all your marks into a couple exams.
I should have mentioned too that the exams were online and they didn't offer any opportunity to show your work, you were given multiple choice questions and that was it.
Topology wasn’t offered in my program, it was always a class I wanted to take. Maybe in my masters program I can see ot
I recommend getting a textbook and teach yourself the material.
He looks like he is already struggling with its Hardness *-*
It wasn't an easy video to make :)
Best part of taking an algebra course was everyone looking at you like you're an idiot taking algebra in junior year. I thought you were a math major? Come on I took that crap in high school lol. So then I'd pull out my copy of Lang and ask for help with a problem.
Combine all this into 1 class, and you have Harvard Math 55
for me graph theory for sure.
can be very tough!
Just graduated with a math degree (June 2022).
This is my list (not in order):
Also keep in mind that I didn’t take ALL math classes since some were math electives.
Hard:
1) Real Analysis
2) Differential Equations
3) Group Theory
Medium:
1) Number Theory
2) Linear Algebra
3) Stats
Easy:
1) All Calculus courses
2) Discrete Math
Unrelated courses:
Hard:
1) Computer Science (c++) (topics I struggled Linear linked lists, external files, and so on) this class was by far the hardest for me
Medium:
1) Architecture (was my major before I switched to math. Not very hard but a lot of time is spent)
2) Biology
Easy)
- All of the general education classes
- writing classes
Overall as a math graduate, many classes for me were easy and I’m surprised how “easy” it was for me. Never really struggled and it’s interesting how other people see math as hard. It’s all about being consistent.
The only class that really gave me a challenge and I didn’t pass, was intro computer science (c++). Which might surprise some people. I was good at math but I guess wasn’t so good with computers. As of now though, I’m confident I could pass if I retook it.
Another class for me that was hard but managed to pass was Real Analysis, Group Theory and Differential Equations.
Abstract Algebra
It's tough!
If you can't write proofs in geometry, introduction to proofs will be the class that makes you change your major from math to something else.
I'm not a math major, but real analysis found a way to ruin my life as well... :D It's kind of interesting, but it's very theoretical IMO, lord knows I can't remember all the proofs...
As a research student i can say Real analysis and abstract algebra sums up the whole universe.... It's just everything around us whether we feel it or not but it is.
What about differential equations and partial differential equations? I found those to be tough since they have a lot of information to cover. All of my proof classes have actually been pretty easy though
Diff Eq is not that bad, as long as you have a solid foundation of Calculus.
Bruh, complex analysis was hella easy and cool.
Glad you enjoyed it!
1.25x speed
I'll try to speak faster in the future :)
Come on
They are all hard. All of math is a struggle 😅
They all certainly can be!
Calculus series is a nightmare, I repeat DON"T TAKE CALCULUS
I'm sorry to hear you had a bad experience with it. Hope you have a nice day!
Abstract Algebra without a doubt was the most difficult. I have a BA and MA in math. That subject alone discouraged me from pursuing a PhD in math. So I got a PhD in Engineering. My favorite topic was Numerical Analysis. Great way to get around theory. I used it a lot in my engineering career.
What was so hard about it, I have to take it soon
every one of them lol
You mean it gets harder than calc 3? Lol jk