Відео

I eye balled the answer as 30% by observing the difference of angle Between 60 degrees at P to (X)M, that seemed to be the most intelligent approach to me, but I don't understand why it looked at the problem this way. I didn't know how to use deduction & logic by following what other information I could see (explicit) to uncover the hidden / unknown value of X(implicit) , thank you. Why does the 4 angles around the centre = 360 degrees yet if you add all the angles for each square it = 700 degrees or is it 720🤭🧐 "mathematics is a game" a game of explicit & implicit players😉

I'm proud of you that you are teaching Mathematics. It is very interesting subject.The way you are teaching ,it's excellent

What software do you use for your working out? Do you use a tablet?

Brilliant explanation! Thank you so much Dr Marrero 👏

WE+C=29WM(SCCP16+88)=<138IPP^©=108$

incredible india..

First you cry, then you give it up, then start again, then kick yourself for being stupid...and finally give it up :))

sir i very thankful from india

Thank you very much for such an amazing video. 🙂

Hello, it's me again. Same basic question: What is a determinant beyond just a number? And what is an inverse matrix beyond just a bunch of numbers in rows and columns? For that matter, what is the original matrix A beyond just numbers? Thanks. In these examples they are attached to equations, which can be represented with a graph. But I know that beyond that they become just numbers, from which more numbers are derived. So I think it's very important to keep referring back to equations, expressions and graphs to put some meaning into them.

OK. Here is the question that has been haunting me for years: What is matrix B? Geometrically. Is it a vector, like the vectors that in physics represent wind and current? If B is two numbers in a column, what would two numbers in a row be? Geometrically. Maybe that is a vector, and B is something else. Please clarify. Ultimately, what is matrix A? Geometrically. Because I can learn to correctly manipulate all these numbers, but I have no idea what they really mean. Thanks.

My teaching experience is explaining the mindset needed to use when understanding a concept . It is the window through which to look to see what is relevant I.e. to identify as you put it connections that will enable you to make sense of what you are experiencing. Taking your example of fractions . A key concept is “ What is a whole?” A whole is not as commonly thought a thing not broken up or one complete thing but can be anything considered as the whole . So a half can be considered as a whole,six eggs can be considered as the whole . This is needed as children will often be presented with whole shapes cut into equal parts when introduced to this idea. This sets the idea that only whole shapes or whole numbers can be the starting point . The notion of equivalent fractions i.e. half is two quarters , three sixths etc can be shown as a line of numerators over denominators and connected with multiplication tables where the one times table is the numerator and two times table the denominator . Another important concept is partition . Here basic numbers can be split so five is three plus two , eight is five plus three but also nine minus one and links up with your example of nine as three squared. I call this numbers in disguise. Inverse as you say is another important idea to understand . Maths unfortunately is like the roots of a plant spreading in lots of directions and all connected but because the emphasis is on natural numbers with counting and basic operations people believe that is all it is and say I was never any good at maths because they could not remember multiplication tables. Yet few are helped by the concept of partition so eight times seven can be split up into five lots of seven plus three 😂lots of seven . Five lots of seven can be thought of as half of as ten lots of seven or seventy . Seven tens shared is three and a half tens or thirty five.

Step 1: Define the Two Integers with Arbitrary Offsets We know 82 82 lies between 𝑛 1 = 81 n 1 ​ =81 and 𝑛 2 = 83 n 2 ​ =83, but let’s complicate things with small offsets: 𝑛 1 = 81.0000000001 , 𝑛 2 = 83.0000000001. n 1 ​ =81.0000000001,n 2 ​ =83.0000000001. Clearly, 82 82 satisfies: 𝑛 1 < 82 < 𝑛 2 , n 1 ​ <82<n 2 ​ , but let’s dissect further. Step 2: Add a Microscopic Floating Buffer Introduce a milli-buffer 𝜖 ϵ, where 𝜖 = 0.00000001 ϵ=0.00000001. Adjust the bounds: 𝑛 1 = 81 + 𝜖 , 𝑛 2 = 83 − 𝜖 . n 1 ​ =81+ϵ,n 2 ​ =83−ϵ. Now we claim 82 82 lies within this "compressed integer range": 81.00000001 < 82 < 82.99999999. 81.00000001<82<82.99999999. Step 3: Define Through Fractions and Rounding Let’s express 82 82 as a weighted average of the bounds: 82 = 𝑛 1 + 𝑛 2 2 + 𝛿 , 82= 2 n 1 ​ +n 2 ​ ​ +δ, where 𝛿 δ is a nano-correction factor for floating-point precision. Using 𝑛 1 = 81.0000001 n 1 ​ =81.0000001 and 𝑛 2 = 83.0000001 n 2 ​ =83.0000001: 82 = 81.0000001 + 83.0000001 2 + 0.0000000001. 82= 2 81.0000001+83.0000001 ​ +0.0000000001. Simplify: 82 = 82.0000001 − 0.0000000001 = 82. 82=82.0000001−0.0000000001=82. Step 4: Overcomplicate the Gap The distance between 𝑛 1 n 1 ​ and 𝑛 2 n 2 ​ is: Δ = 𝑛 2 − 𝑛 1 = 83.0000000001 − 81.0000000001 = 2.0000000000. Δ=n 2 ​ −n 1 ​ =83.0000000001−81.0000000001=2.0000000000. Position 82 82 proportionally within this gap: Position = 82 − 𝑛 1 Δ . Position= Δ 82−n 1 ​ ​ . Substitute: 82 − 81.0000000001 2.0000000000 = 0.9999999999 2.0000000000 = 0.49999999995. 2.0000000000 82−81.0000000001 ​ = 2.0000000000 0.9999999999 ​ =0.49999999995. So 82 82 is exactly halfway, with nano-level accuracy, between 𝑛 1 n 1 ​ and 𝑛 2 n 2 ​ . Step 5: Make a Grand Conclusion After an absurd amount of effort, we confidently state: 82 lies between 81.0000000001 and 83.0000000001. 82 lies between 81.0000000001 and 83.0000000001. And the two integers are (drumroll, please): 81 and 83. 🎉 You said: I think I forgot the divide thingy ChatGPT said: ChatGPT Ah, you're saying you forgot the divide thingy? No problem! Let's mix that back into this unnecessarily complex determination of which two integers 82 𝑋 X 82 ​ is between, using small numbers and big chaos. 😄 Step 1: Write It as a Fraction We want to determine where 82 𝑋 X 82 ​ falls between two integers. Assume 𝑋 X is some positive value that splits 82 82: 82 𝑋 = 𝑁 , where 𝑁 is the range we’re working with. X 82 ​ =N,where N is the range we’re working with. For now, we’ll pretend 𝑋 X is approximately 10.00001 10.00001. Step 2: Estimate 𝑁 N with Tiny Deviations Using 𝑋 = 10.00001 X=10.00001, calculate: 82 10.00001 ≈ 8.199999180000. 10.00001 82 ​ ≈8.199999180000. Clearly, 8.19999918 8.19999918 is between two integers: 8 and 9. 8and9. Step 3: Add Microscopic Errors Let’s distort 𝑋 X by introducing a milli-offset: 𝑋 = 10.00001 + 𝜖 , where 𝜖 = 0.0000001. X=10.00001+ϵ,where ϵ=0.0000001. Recompute: 82 𝑋 = 82 10.00001 + 0.0000001 ≈ 8.199999091. X 82 ​ = 10.00001+0.0000001 82 ​ ≈8.199999091. This new value still lies between 8 and 9, but now we’ve made it nano-accurate. Step 4: Test Nearby Divisors Try slightly smaller divisors like 𝑋 = 9.99999 X=9.99999: 82 9.99999 ≈ 8.2000018. 9.99999 82 ​ ≈8.2000018. Now 82 𝑋 X 82 ​ skews closer to 8.2 8.2, but it’s still comfortably nestled between: 8 and 9. 8and9. Step 5: Grand Complication with Rounding Introduce a rounding error to further muddy the waters: 𝑁 = round ( 82 10.00001 − 𝜖 ) . N=round( 10.00001−ϵ 82 ​ ). For 𝜖 = 0.00000001 ϵ=0.00000001: 82 10.00001 − 0.00000001 ≈ 8.199999999. 10.00001−0.00000001 82 ​ ≈8.199999999. Rounding places 𝑁 N firmly between 8 and 9. Final Conclusion Whether through precise division, milli-offsets, or rounding madness: 82 𝑋 lies between 8 and 9. X 82 ​ lies between 8 and 9. 🎉 Let’s call this a victory for math and unnecessary complexity!

Hi Sir I would join Sir

Wow such nice approach learning maths.. I wish i knew earlier.. My problem was, i didn't practise enough and then as we moved to higher classes forgot old formulas.. And concepts... Like exponential function and differentiation formula.

I loved your lecture!! Truly! However, I really, really found your piano music distracting! At one point I could not hear what you were saying. :lease remember the volume isn't the same on every computer. Please take the time to edit the background "music" out

Thank you, just wondering which application you are using in the video 😊

I would love to join you too

Good points... :) The best way to learn not only maths, but any subject for that matter is to learn 'in layers'. Don't try to master one particular subject or topic or aspect at once. First familiarize with the keywords (jargon) in that subject (maths for example). Familiarity alone breeds ease. Try to get the intuitive idea about each concept/topic/keyword. Inter-relate them. Find about other concepts related to it. You first need to see the big picture. Forget the hard and formal definitions. Specially in maths, there is always much simple and intutitive way of interpreting and understanding the concepts (even the so-called abstract concepts). Actually you can easily and intuitively understand maths (even quantum physics). But if you want to be an expert, you must solve hundreds, if not thousands of examples.

Math teachers should step by step to tech the TECHNOLOGY of solving math problems , by other words , to guide brain steps of student thinking to the AHA moments.

Attitude is everything. If you don’t enjoy what you’re doing you need to be doing something else.

Name of this wonderful piano piece ?

No, no, no. Abstraction does not come from reality. Mathematics is not about reality. We apply the abstractions of mathematics to the physical world. Numbers and their arithmetic operations are eternal. You don't have even have to think of as they exist indefinitely as noumena (well-formed concepts). Of course, many things that are called 'number' today are not numbers, but that is a different topic. Τὰ Στοιχεῖα Εὐκλείδου δὲν εἶναι Γεωμετρία (οὔτε ἐπιπεδομετρία, οὔτε γεωμετρία χώρου), ἁπλῶς μποροῦν νὰ παραχθοῦν ἀπὸ αὐτὰ «Γεωμετρίες» (εἴτε «Εὐκλείδειες», εἴτε «μὴ Εὐκλείδειες», κλπ), ὅπως ἐπίσης μποροῦν νὰ παραχθοῦν πολλές ἄλλες θεωρίες «Μαθηματικές» καὶ ὄχι μόνο, π.χ. Θεωρία Ἀριθμῶν, Ἀναλογίες, Ἀσύμμετρα Μεγέθη, Θεωρία τῆς Σχετικότητας, κ.α. Τὰ Στοιχεῖα τοῦ Εὐκλείδου δὲν εἶναι οὔτε ἀντικείμενα τοῦ Πραγματικοῦ κόσμου, καὶ οὔτε εἶναι ἀντικείμενα τῶν Μαθηματικῶν, ἀλλὰ χωρίς αὐτὰ, ὅλα τά παραπάνω δὲν μποροῦν νὰ περιγραφοῦν, νὰ κατανοηθοῦν, νὰ ἑρμηνευτοῦν. Πολλοί συγχέουν τον πραγματικό χῶρο τῶν «Φυσικῶν» ἐπιστημῶν με τὰ Στοιχεῖα Εὐκλείδου. Ἀπὸ τα Στοιχεῖα Εὐκλείδου προέρχονται οἱ πλεῖστες μαθηματικές καὶ φυσικές ἐπιστῆμες, τόσο οἱ παραδοσιακές ὅσο καὶ οἱ μοντέρνες. Γιὰ τις τεχνολογίες αὐτὸ εἶναι προφανές Τα Στοιχεῖα Εὐκλείδου ἀποτελοῦν ἕνα ἑνιαῖον ὅλο, ἕνα «Σύστημα», τὸ ὁποῖο εἶναι «κλειστό καὶ ἀνοικτό», τόσο ὅσο καὶ ἡ σκέψη, ὁ λόγος καὶ ἡ γραμματική τῆς ἀνθρώπινης ὑπόστασης. Ἡ πληρότητα καὶ ἡ συνέπεια εἶναι δομημένες μὲ ἕναν ἐκπληκτικὸ τρόπο, ποὺ τὸ καθιστοῦν μοναδικό. Τὸ θεώρημα τοῦ Gödel δὲν μπορεῖ νὰ ἐφαρμοστεῖ στὰ «Στοιχεῖα», γιατί τὸ «Μηδέν» καὶ τὸ «Ἄπειρο», ἐνῶ χρησιμοποιοῦνται, δὲν ὁρίζονται ὡς «στοιχεῖα». www.physics.ntua.gr/~mourmouras/euclid_desktop/common/anti_prologou.html I'll translate the following for you: Τὰ Στοιχεῖα τοῦ Εὐκλείδου δὲν εἶναι οὔτε ἀντικείμενα τοῦ Πραγματικοῦ κόσμου, καὶ οὔτε εἶναι ἀντικείμενα τῶν Μαθηματικῶν, ἀλλὰ χωρίς αὐτὰ, ὅλα τά παραπάνω δὲν μποροῦν νὰ περιγραφοῦν, νὰ κατανοηθοῦν, νὰ ἑρμηνευτοῦν. Translation: Euclid's Elements are neither objects of the Real World, nor are they objects of Mathematics, but without them, all of the above cannot be described, understood, or interpreted. Me: The Elements of Euclid are discovered from 100% pure Ancient Greek thought. They are abstract. Euclid's Elements are not Geometry (neither plane geometry nor spatial geometry), they can simply produce "Geometries" (either "Euclidean", or "non-Euclidean", etc.), just as they can produce many other "Mathematical" theories and not only, e.g. Number Theory, Analogies, Asymmetric Quantities, Theory of Relativity, etc.

Years out of school, I read that lots of math teachers in high school in the USA were actually non math majors but had minors in math, so got pressed into service by the school bureaucracy. Hence the people supposed to teach you the invaluable basics amounted to a cyclops leading the blind. What resulted is people blaming themselves for being bad in math, rather than fixing the system of teaching math. Proof is how school system exiled Hymie Escalante, the teacher who taught AP calculus in poverty stricken east Los Angeles. See movie Stand and Deliver.

Dejé el link del curso 😊

A fraction is a just *number* : 1/2 = Measure ( _ : _ _) 0.5 is the measure of 1/2 in base 10: (1/2 x 10/10) = (10/2 x 1/10) = 5 x 1/10 = 0.5 7:21 Yes, a number is used to model all those concepts and to make sense of the physical world around us. The connection is Euclid's Elements Book V and Proposition 12. I define number correctly as follows: A number is a NAME given to a MEASURE that describes a RATIO of MAGNITUDES. I can teach YOU exactly why you do the things that you do. For example, I can show you why p/q ± r/s = (ps±rq)/(qs), p/q ÷ r/s = (ps)/(qr) and why p/q x r/s = (pr)/(qs) without even using numbers! Only geometry. I have a feeling you are the kind of man who would like to know these things. I can show you the entire development of number in 7 steps. First 4 are geometry and last 3 are algebra. In algebra, we sacrifice precision for generality. Algebra is a weaker form of geometry. Interested? Contact me!

When I was in the first grade (1976-77), among other things, I was told that 2+3=5, and that 3 +2=5. I reasoned that 2+3=3+2. Eight years later, this was confirmed in an algebra class. I kept it to myself, because I didn't see the connection at six years old. Instead, I used this bit of information all throughout those eight years. It never occurred to me that math was difficult until I got to algebraic word problems; the method for solving them was never explained in a way that made sense to me, and while it didn't get in the way of my love for the subject, it had me questioning my intelligence for decades. To this day, I'm still struggling with calculus, not because it's difficult, but because there's something in my mind that tries to tell me I'm not capable of taking words and transforming them into useful formulas. Therapy remains an option...

Sir, i love your way to teach math, it is superb!!

Good video!

I really respect teacher who love their students !

Great teaching sir i like the idea of what else

As a math enthisiast I enjoyed your video. I've seen the graphic proof that starts with the 4 triangles at the corners of the large square. The proof then moves / slides the top 2 triangles to the diagonally to the opposite corners, respectively. One then sees 2 sets of triangles forming 2, (a x b), rectangles, one verticle (v) and one horizontal (h). The (c x c) center area has shifted to 2 smaller squares; (a x a) above the (v) rectangle, and (b x b) above the (h) rectangle.

a great video i am from Pakistan and i want from your channel to have the pattern for mathematics from start to finish not any random concept

Thank you for your videos. Sir, If it's possible for you then can you make videos on "How to read and understand Undergraduate and Graduate level difficult mathematics textbook in self study mode?"

Excellent Video. If math was ever taught like this , I wish that class would never end. I am going to do some math now and look forward to other such works as your subscriber

Dr. Marrero, you're a good teacher! Keep making such videos. When you teach, I can feel the love and passion you have for the subject. I would be happy to listen to your podcast.

Amazing take on so called "Math Anxiety" Dr. Marrero....Could you please tell me which "whiteboard app" are you using?

What a beautiful work of art this video is! I am a physics student at the University of Zurich in Switzerland. I struggled a lot in my first year of the Bachelors, especially with Linear Algebra and Analysis. For me the trick was just to have fun doing math. Math for me is about exploring different ideas and about thinking. I was always an overthinker and now I've managed to direct this into thinking about math and the world in general, questioning things and thinking about why things are the way they are. There is so much more to say, but to summerize, I think the way I learned math is I learned to love it, the rest comes along :D

just really struggled on this exact problem on my practice sat rn. very simple thank you

Let me explain to you how I learned mathematics. I used math books to define the definition of mathematics, then I used philosophy to understand the concepts of mathematics. After reading and buying hundreds and hundreds of mathematical calculus books, I observed that nature was pure mathematics. I was astonished that upper level mathematics depended heavily on all the principles of the connecting pieces of a puzzle, but if you understand the big picture you will undoubtedly reach the level of mathematics that is magical. Therefore after years and years of learning the Fibonacci sequence, it dawned on me that math is universal, and that the absolute value of truth is a reflection of the universe.

Thank Prof ❤

Wooow. This is amazing 🔥