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Mu Prime Math
United States
Registrace 12. 11. 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: czcams.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: czcams.com/play/PLug5ZIRrShJGFne7YhMi-4eYsUKzkITao.html
Subscribe to see more new math videos!
Music: C418 - Pr Department
zhlédnutí: 3 686
Video
Proof: Uniqueness of the Tensor Product
zhlédnutí 2,3KPřed rokem
Universal property introduction: czcams.com/video/vZzZhdLC_YQ/video.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: czcams.com/play/PLug5ZIRrShJHCtzgzZyRq...
Tensor Product Basis With the Universal Property
zhlédnutí 3,3KPřed rokem
Tensor product universal property explanation: czcams.com/video/vZzZhdLC_YQ/video.html Generating set proof: czcams.com/video/KnSZBjnd_74/video.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
zhlédnutí 7KPřed rokem
Previous tensor product video: czcams.com/video/KnSZBjnd_74/video.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
zhlédnutí 1,6KPřed rokem
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: czcams.com/play/PLug5ZIRrShJHDvvls4OtoBHi6cNnTZ...
Why can we change lim n→∞ to lim x→∞?
zhlédnutí 2,2KPřed rokem
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: czcams.com/play/PLug5ZIRrShJGFne7YhMi-4eYsUKzkITao.html Subscribe to see more new ma...
A Natural Proof of the First Isomorphism Theorem (Group Theory)
zhlédnutí 7KPřed rokem
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: czcams.com/play/PLug5ZIRrShJHDvvls4OtoBHi6cN...
Integral Formula for Natural Log (without knowing the derivative)
zhlédnutí 3,2KPřed rokem
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
zhlédnutí 3,8KPřed 2 lety
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
zhlédnutí 3,4KPřed 2 lety
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?
zhlédnutí 3,6KPřed 2 lety
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
zhlédnutí 13KPřed 2 lety
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: czcams.com/play/PLug5ZIRrShJHNCfEiX6l5CKbljWayGEcs.html Subscribe to see more new math videos! Music: C418 - Pr De...
My favorite proof of the n choose k formula!
zhlédnutí 39KPřed 2 lety
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: czcams.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?
zhlédnutí 4,8KPřed 2 lety
Epsilon-Delta definition explanation: czcams.com/video/JbbRaiXI6yw/video.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: czcams.com/play...
Why can't we group the terms in 1-1+1-1+... ?
zhlédnutí 2,7KPřed 2 lety
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: czcams.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?
zhlédnutí 4,5KPřed 2 lety
When can we switch the limit and function?
Topology Definitions: Closure, Boundary, Interior
zhlédnutí 20KPřed 2 lety
Topology Definitions: Closure, Boundary, Interior
Why can we do this to find inverse functions?
zhlédnutí 2,2KPřed 2 lety
Why can we do this to find inverse functions?
Bijective Functions Have a Two-Sided Inverse
zhlédnutí 2,3KPřed 2 lety
Bijective Functions Have a Two-Sided Inverse
Proof: Two-Sided Inverse Functions are Unique
zhlédnutí 2,5KPřed 2 lety
Proof: Two-Sided Inverse Functions are Unique
Sum of natural numbers equals n+1 choose 2!
zhlédnutí 5KPřed 2 lety
Sum of natural numbers equals n 1 choose 2!
Representation Theory: Irreducible Characters Are an Orthonormal Basis
zhlédnutí 1,3KPřed 2 lety
Representation Theory: Irreducible Characters Are an Orthonormal Basis
Matrix Invertibility With F[x]-Modules
zhlédnutí 1,2KPřed 2 lety
Matrix Invertibility With F[x]-Modules
Difference Between Normalizer, Centralizer, and Stabilizer
zhlédnutí 8KPřed 2 lety
Difference Between Normalizer, Centralizer, and Stabilizer
A Concrete Introduction to Tensor Products
zhlédnutí 47KPřed 2 lety
A Concrete Introduction to Tensor Products
The Cayley-Hamilton Theorem is Easy with F[x]-Modules
zhlédnutí 2,3KPřed 3 lety
The Cayley-Hamilton Theorem is Easy with F[x]-Modules
How the Matrix Characteristic Polynomial is Connected to F[x]-Modules
zhlédnutí 1,4KPřed 3 lety
How the Matrix Characteristic Polynomial is Connected to F[x]-Modules
F[x]-Module Derivation of Rational and Jordan Canonical Forms
zhlédnutí 3KPřed 3 lety
F[x]-Module Derivation of Rational and Jordan Canonical Forms
I am perpetually confused
automatic korean subtitles? kekeke
You explain this far better than my university lecturer.
Is there not any theorem as - ℒ⁻¹{∫[s ∞] f(u) du} = F(t)/t
thank you for content . I hope you will continue make such content, especially about abstract theories (Group theory, Topology, Abstract Algebra etc)
Thank you
This came in jee mains 2016
perfect explanation
You have a deep understanding of the subject.
That's what I just needed thanks
Please come back and enlighten us again :(
Great video bro
Great work
Wow this video is the best explanation on Laplace transform! Thank you! Can you also do a derivation for Fourier Transform please ??
crystal clear, thank you!
Excellent! Thanks a lot!
very nice 👌
Beautiful 🎉
I love you
pls collab with qncubed3
Perhaps use the symmetry of ln(x) and e^x, lol, or something...it should be the same as the integral from -1 to 0 of e^x, no?...Lol...perhaps I'm making some mistake here...
I am probably too stupid to understand this. Some people computing the curl, some people don‘t.
That was really clear. Good stuff.
Most cutest mathematics teacher ❤❤❤❤❤❤❤
Fabulous 👌
So the reason I was having trouble visualizing a surface integral is because I'm not a 4-dimensional being. That makes sense.
Great
where can i get that shirt?
This is fire thank you. Perfectly rigorous with great examples.
Your remark at 6:25 confused me at first. You'd have 0 === 0 mod 0, and from that you'd say 0 divides 0-0, but the trick is, you can't divide by 0, so 0/0 is undefined.
I found the third proof the most interesting and creative. How mathematicians figure out what to just "pull out of the ether" in this case adding -bc+bc is really astounding. What separates amateurs like myself from the pros
So you can multiply both sides of a === b (mod) n by the same number or 2 special congruent numbers of the same n, but not necessarily any old set of numbers.
Thank you for these videos, I was studying cryptography and it assumes you know a lot about modular arithmetic. I took a lot of math in primary school and college, and I don't seem to recall ever going through this (but I never took a cryptography course to be fair, and I could have forgotten about it)
very good explanation. Thank You for explanation.
the way you hold the marker is very distracting
I just write a % n instead of rem(a,n) when I'm working out math on paper, I just use the C notation, it's succinct.
I wish I found this video before my midterm.... I got it for my finals though 😃
amazing!!!
Thank you
😮
Very Good Explanation of Laplace Transform to Visualize.
At 7:00 , shouldn't the parallelogram's endpoints be r(u, v), r(u+du, v) etc?
That's correct. As is implied at 4:09, I'm using the ordered pairs as shorthand for the corresponding points on the surface.
Sounds like the dot product of orthonormal basis vectors. Either 0 if they are distinct or 1 if they are the same... is there any relation?
I love how you always give a quick review on the process at the end 😊
👍
6.6k views and only 17 comments? Let me fix that
it's very easy to evaluate this intégral by parts you complicated it man
😮
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Hi sorry what text are you working off of?
This video wasn't working off of any particular text.