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Mu Prime Math
United States
Приєднався 12 лис 2018
Mu Prime Math is a library of math explanation videos.
Many of my videos cover interesting challenge problems with solutions that require unexpected shifts in perspective. I have playlists for challenging pre-calculus problems, integrals, and calculus problems like infinite series and differential equations!
I also have several series dedicated to intuitively explaining ideas in specific areas of math. I've made playlists on differential equations, linear algebra, and vector calculus. These videos emphasize understanding where formulas and methods come from and why they work, so you can build a base of knowledge that extends into higher mathematics!
Many of my videos cover interesting challenge problems with solutions that require unexpected shifts in perspective. I have playlists for challenging pre-calculus problems, integrals, and calculus problems like infinite series and differential equations!
I also have several series dedicated to intuitively explaining ideas in specific areas of math. I've made playlists on differential equations, linear algebra, and vector calculus. These videos emphasize understanding where formulas and methods come from and why they work, so you can build a base of knowledge that extends into higher mathematics!
Does the Gaussian integral trick work for other functions?
Proof for Riemann-integrable functions:
Robert J. MacG. Dawson. “On a “Singular” Integration Technique of Poisson”. American Mathematical Monthly, 2005. cs.smu.ca/~dawson/Poisson.pdf
We can compute the integral of e^(-x^2) using a very cool trick that lets us switch to polar coordinates and use the Jacobian for a u-sub. But does this technique work for any other function? In this video we turn that problem into a differential equation and find all of the solutions!
Mariano Suarez-Alvarez's proof: math.stackexchange.com/a/4517530/713547
0:00 The Functional Equation
4:23 The Differential Equation
7:14 Solving
12:34 Additional Notes
Calculus Problems playlist: ua-cam.com/play/PLug5ZIRrShJGFne7YhMi-4eYsUKzkITao.html
Subscribe to see more new math videos!
Music: C418 - Pr Department
Robert J. MacG. Dawson. “On a “Singular” Integration Technique of Poisson”. American Mathematical Monthly, 2005. cs.smu.ca/~dawson/Poisson.pdf
We can compute the integral of e^(-x^2) using a very cool trick that lets us switch to polar coordinates and use the Jacobian for a u-sub. But does this technique work for any other function? In this video we turn that problem into a differential equation and find all of the solutions!
Mariano Suarez-Alvarez's proof: math.stackexchange.com/a/4517530/713547
0:00 The Functional Equation
4:23 The Differential Equation
7:14 Solving
12:34 Additional Notes
Calculus Problems playlist: ua-cam.com/play/PLug5ZIRrShJGFne7YhMi-4eYsUKzkITao.html
Subscribe to see more new math videos!
Music: C418 - Pr Department
Переглядів: 3 510
Відео
Proof: Uniqueness of the Tensor Product
Переглядів 2,1 тис.Рік тому
Universal property introduction: ua-cam.com/video/vZzZhdLC_YQ/v-deo.html This video proves the uniqueness of the tensor product of vector spaces (or modules over a commutative ring). This uses the universal property of the tensor product to prove the existence of an isomorphism (linear bijection) between any two "tensor products". Tensor Products playlist: ua-cam.com/play/PLug5ZIRrShJHCtzgzZyRq...
Tensor Product Basis With the Universal Property
Переглядів 3 тис.Рік тому
Tensor product universal property explanation: ua-cam.com/video/vZzZhdLC_YQ/v-deo.html Generating set proof: ua-cam.com/video/KnSZBjnd_74/v-deo.html timestamp 23:57 If we have a basis for each of two vector spaces (or modules over a commutative ring) V and W, then we can use that to form a basis for the tensor product V⊗W. The proof uses the universal property of the tensor product, which conne...
Complete Derivation: Universal Property of the Tensor Product
Переглядів 7 тис.Рік тому
Previous tensor product video: ua-cam.com/video/KnSZBjnd_74/v-deo.html The universal property of the tensor product is one of the most important tools for handling tensor products. It gives us a way to define functions on the tensor product using bilinear maps. However, the statement of the universal property can be confusing if it is presented without background. This video is an explanation o...
How to Define Homomorphisms on Quotient Groups
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One way to define a function on a quotient group is to define it in terms of the coset representatives. However, this approach runs into problems of well-definedness. This video explains how we can address that problem. 0:00 Problem Introduction 5:42 Solution 10:34 Non-example: Integers mod 5 11:13 Example: Alternating Group Group Theory playlist: ua-cam.com/play/PLug5ZIRrShJHDvvls4OtoBHi6cNnTZ...
Why can we change lim n→∞ to lim x→∞?
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When computing the limit of a sequence, it's often useful to consider a limit of real numbers so that we can do things like take derivatives. But why is this allowed in the first place? Why can we change a limit of integers to a limit of real numbers? This video gives an explanation. Calculus Problems playlist: ua-cam.com/play/PLug5ZIRrShJGFne7YhMi-4eYsUKzkITao.html Subscribe to see more new ma...
A Natural Proof of the First Isomorphism Theorem (Group Theory)
Переглядів 6 тис.Рік тому
The first isomorphism theorem is one of the most important theorems in group theory, but the standard proof may seem artificial, like every step of the proof is set up knowing that we're trying to create an isomorphism. In this video, we show an alternate proof with no such tricks using the preimage map of a group homomorphism. Group theory playlist: ua-cam.com/play/PLug5ZIRrShJHDvvls4OtoBHi6cN...
Integral Formula for Natural Log (without knowing the derivative)
Переглядів 3,1 тис.Рік тому
This video proves that the natural log equals the integral from 1 to x of 1/t dt under the assumption that ln(x) is the inverse function to the exponential e^x. We can do this without already knowing the derivative of the natural log! More details on why the integral is the inverse of e^x: We proved in the video that any right inverse to e^x must equal that integral. However, we didn't prove th...
Supremum, Infimum: Definition and Explanation
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Not all sets of real numbers have a maximum and a minimum. In this video, we introduce the supremum and infimum as a generalization of max and min. Sup and inf appear everywhere in analysis. Subscribe to see more new math videos! Music: OcularNebula - The Lopez
Topology Definitions: Connected and Path-Connected
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Connectedness is a key idea in topology and metric spaces that describes whether a topological space can be separated into two components. This video explains the open set definition of connectedness and describes the topologist's sine curve as a non-example that motivates the definition of path-connectedness. Timestamps: 0:00 connectedness 9:59 path-connectedness Subscribe to see more new math...
Does 1+2+3+...=-1/12?
Переглядів 3,5 тис.2 роки тому
The answer to the question in the title is that it depends on how you define the infinite sum function. Until the infinite sum function is specified, the question is not well-defined; it's the equivalent of asking "what is f(5)?" without defining the function f. The sum of all natural numbers, and the sums of divergent series more generally, are often debated because it seems incoherent to say ...
Proof: Orthogonal Matrices Satisfy A^TA=I
Переглядів 12 тис.2 роки тому
One way to characterize orthogonal matrices is to say that a matrix orthogonal if and only if A transpose times A is the identity matrix. In this video, we prove this result using basic matrix calculations and the definition of orthonormal vectors. Learning Linear Algebra playlist: ua-cam.com/play/PLug5ZIRrShJHNCfEiX6l5CKbljWayGEcs.html Subscribe to see more new math videos! Music: C418 - Pr De...
My favorite proof of the n choose k formula!
Переглядів 37 тис.2 роки тому
The binomial coefficient shows up in a lot of places, so the formula for n choose k is very important. In this video we give a cool combinatorial explanation of that formula! Challenge Problems playlist: ua-cam.com/play/PLug5ZIRrShJGkzGsXMYQt8bi5ImYtiEMM.html Subscribe to see more new math videos! Music: OcularNebula - The Lopez
Epsilon-Delta proofs: Can't we make the limit equal anything?
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Epsilon-Delta definition explanation: ua-cam.com/video/JbbRaiXI6yw/v-deo.html Proofs that use the delta-epsilon definition of the limit can be confusing because it seems like we can prove that the limit is anything we want if we pick the right value of delta. In this video we prove that limits are unique and go over some examples of disproving limits! Calculus Problems playlist: ua-cam.com/play...
Why can't we group the terms in 1-1+1-1+... ?
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We can group the terms in the divergent infinite sum 1-1 1-1 ... to get a value of zero or a value of one, even though the series doesn't converge. This video gives an explanation of why grouping terms in Grandi's series doesn't give the correct answer. Calculus Problems playlist: ua-cam.com/play/PLug5ZIRrShJGFne7YhMi-4eYsUKzkITao.html 0:00 Why the sum diverges 7:33 Why grouping fails 12:57 Whe...
When can we switch the limit and function?
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When can we switch the limit and function?
Topology Definitions: Closure, Boundary, Interior
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Topology Definitions: Closure, Boundary, Interior
Why can we do this to find inverse functions?
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Why can we do this to find inverse functions?
Bijective Functions Have a Two-Sided Inverse
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Bijective Functions Have a Two-Sided Inverse
Proof: Two-Sided Inverse Functions are Unique
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Proof: Two-Sided Inverse Functions are Unique
Sum of natural numbers equals n+1 choose 2!
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Sum of natural numbers equals n 1 choose 2!
Representation Theory: Irreducible Characters Are an Orthonormal Basis
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Representation Theory: Irreducible Characters Are an Orthonormal Basis
Matrix Invertibility With F[x]-Modules
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Matrix Invertibility With F[x]-Modules
Difference Between Normalizer, Centralizer, and Stabilizer
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Difference Between Normalizer, Centralizer, and Stabilizer
A Concrete Introduction to Tensor Products
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A Concrete Introduction to Tensor Products
The Cayley-Hamilton Theorem is Easy with F[x]-Modules
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The Cayley-Hamilton Theorem is Easy with F[x]-Modules
How the Matrix Characteristic Polynomial is Connected to F[x]-Modules
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How the Matrix Characteristic Polynomial is Connected to F[x]-Modules
F[x]-Module Derivation of Rational and Jordan Canonical Forms
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F[x]-Module Derivation of Rational and Jordan Canonical Forms
Legend
thankyou my lord ♥
Great explanation!
Thank you for the delicate demonstration
Thanks! Extremely clear and concise explanation.
What is the music that is playing at the end of the video? It's interesting.
Check the description!
Please don't use your finger to wipe the board, oil from the skin ruins the pen and the board
Great explanation! Thank you
I got the eigenvector associated to the eigenvalue -2 equal to (1, -4/3), is this okay?
Yes. Any scalar multiple of an eigenvector is also an eigenvector with the same eigenvalue.
I don't follow this last equality that : a x (b sin(theta) ) = a x b , where a and b are vectors. This is sloppy. Because theta is between 0 and 180 degrees, sin(theta) is between 0 and 1. This means that the vector "b sin(theta) " is in the exact same direction as b but is shorter. This means that the area of the parallelogram formed with sides "a" and "b sin(theta)" is smaller than the area of a parallelogram with sides "a" and "b".
The vector over b in b sin θ at 5:40 is a typo. The intent was to say that the length of that orthogonal vector equals the length of b times sin θ. The cross product a × b equals the cross product of a with that orthogonal component.
Hey, thanks for the thorough explanations, it actually makes sense. One question, how do you get the exact error of taylor series in the integral form? could you perhaps send me the video link or any paper for the derivation of the equation? thanks!
고정된 상수값을 원으로 생각하니 이해가바로되네요!
Differentiating Integration of Integral
Feels like he's a right handed and trying to be left handed.
English is not my first language but bro was amazing
I think we can add negative terms like e^-x, e^(-x/2), e^(-x/3), … to the sum to make it converge on the positive side as far as it does on the negative side, even with a finite number of terms
u just made this make sence thank you thank you
Sir please explain the base system and conversion btw different bases
Amazing. Masha allah. Can you explain how your thought process work or how you approach problems. So we can follow it and get some good GPA
I spent four years doing a physics degree starting in 2003. UA-cam existed since 2005 and this sort of content was certainly not available until after I finished. I always found the unengaging lectures difficult to follow, printed lecture notes missing insight and text books impossibly heavy. I wonder how much more I could have got out of that education had content like this been around to enhance conceptual understanding .
I could not understand injection mod n
9:23 r subi is not a divisor of a
any more advanced algebra videos you can do ... please do! These videos are great
thankU love from INDIA
LEFT HANDED AND BEING A MATHEMATICIAN IS TRULY A GIFT
Thank you for posting this video! I've been searching for the geometric Interpretation of determinants for 3x3 matrices and this video nails it.
Thank you!!!
Love your videos. All are well done and clearly presented. Wish you are well; as I saw that the last video was a year ago.
Thank you
Great work ! Ty so mutch . Love from a future chemeng
It's easy to show the square root of any prime number is irrational. Any number can be expressed as the product of prime numbers raised to some non-zero power. If, for some number n, all those exponents are even integers then n is a perfect prime. If one or more of the exponents is odd, n is not a perfect square. Then, when you take the square root of n you're left with at least one square root of a prime number in the product; i.e. an irrational number. So the square root of n is irrational.
Nice:) Thank you so much!!
Nonsense. Now redo the math but don't make the light have a 1:1 ratio on your graph. I like to draw light velocity practically along the x axis, because nothing can go faster. This gives me the full plotting area to enter real data. Not only half of it. The weird way you choose to have light at 45 degrees is the only reason you math works the way it does. You have (minkowski has) created a "special case". Only if light is drawn at 45 can you get the result you want to see. The whole theory collapses if you change that one thing.
Are you writing this on your wall?
I'm using a stick-on whiteboard from writeyboards.com
@@MuPrimeMath oh alr thanks
I will need to look this over a few times and digest it a bit, but it sure seems to be helpful for understanding the function and purpose of normal subgroups, which I darn sure have been stuck on for a long time. Thanks for the upload.
Amazing
Not visible
Lmao.
3:48 I don't understand why do you say that x' = e^(rt) but not x' = e^(At). Why r = A? Or rather, why e*I = A?
Fantastic explanation thank you so much
Excellent excellent excellent, I loved how you explained EVERYTHINGGGGGGGGGGGGGG!!!!!!!!!!! Thank you.
Thanks alot
Nice. Setting aside the pretty poorly drawn parallelograms, this is a slick proof.
too many proofs of v tensor 0 is 0 😂
This channel should get more views. All of the videos are too intuitive and amazing. You explained the main things and confusions within few minutes. That is incredible.
For the most part, trig functions will diverge unless you multiply it with something that converges
You're so amazing i love you
Thx to this proof.in short if p is divisible by q then n will be perfect square but if p is not divisible by q we have a fraction which can be simplified to other or not.in both case n will be a fraction not integer so contradiction and then wron assumption
It's absolutely Rong!