User littleO - Mathematics Stack Exchange

161 votes

Please explain the intuition behind the dual problem in optimization.

answered Jan 2, 2014 at 6:04

123 votes

How would you discover Stokes's theorem?

answered Dec 4, 2021 at 8:27

87 votes

What are some examples of mathematics that had unintended useful applications much later?

answered Sep 7, 2013 at 22:52

78 votes

Accepted

Why does the fundamental theorem of calculus work?

answered Nov 20, 2015 at 1:33

52 votes

Why is $A^TA$ invertible if $A$ has independent columns?

answered Jun 26, 2016 at 23:57

52 votes

What is the Jacobian matrix?

answered Jan 31, 2015 at 4:42

52 votes

Why do we use trig functions in Fourier transforms, and not other periodic functions?

answered Apr 12, 2018 at 8:52

49 votes

Accepted

Intuitive proof of multivariable changing of variables formula (Jacobian) without using mapping and/or measure theory?

answered Aug 11, 2013 at 12:22

48 votes

Accepted

Transpose of block matrix

answered Nov 28, 2012 at 6:04

38 votes

What is integration by parts, really?

answered Jun 9, 2014 at 8:55

38 votes

How to prove Lagrange multiplier theorem in a rigorous but intuitive way?

answered Apr 27, 2016 at 7:36

38 votes

What are some mathematical topics that involve adding and multiplying pictures?

answered Mar 15, 2018 at 22:01

35 votes

Accepted

Does it make sense to learn mathematical concepts as you encounter them rather than in a fixed progression?

answered Dec 24, 2018 at 7:39

33 votes

When has one sufficiently mastered an area of mathematics?

answered Aug 7, 2015 at 7:05

32 votes

Accepted

Intuition behind chain rule

answered Mar 25, 2014 at 9:55

28 votes

Is there a mathematical notation of indexing a matrix?

answered May 11, 2016 at 12:38

28 votes

Accepted

How to physically interpret conjugate functions?

answered Apr 10, 2017 at 0:33

23 votes

Accepted

Why does the Cholesky decomposition requires a positive definite matrix?

answered Aug 8, 2013 at 12:11

23 votes

Why must the gradient vector always be directed in an increasing direction?

answered Oct 27, 2012 at 8:15

22 votes

How does Cramer's rule work?

answered Sep 26, 2016 at 1:47

22 votes

Is basis change ever useful in practical linear algebra?

answered Apr 13, 2016 at 1:26

22 votes

Intuition behind logarithm change of base

answered Dec 28, 2017 at 2:38

21 votes

What are some interpretations of Von Neumann's quote?

answered Nov 20, 2016 at 20:36

21 votes

Why is this allowed? ("Fourier's Trick"; finding the coefficients in a Fourier Series)

answered Mar 9, 2014 at 9:38

21 votes

Accepted

How to expand equation inside the L2-norm?

answered Jul 18, 2014 at 0:44

20 votes

Mathematics - The big picture

answered Aug 18, 2014 at 20:03

20 votes

Accepted

Is there a mathematical notation for restricting the depth of a factorial?

answered Dec 23, 2020 at 17:56

19 votes

Better Proofs Than Rudin's For The Inverse And Implicit Function Theorems

answered Jan 17, 2022 at 1:51

19 votes

Accepted

Why do we need to define Lebesgue spaces using equivalence classes?

answered Apr 11, 2018 at 13:44

19 votes

Big list of "guided discovery" books

answered Jan 15, 2015 at 6:40

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1,081 Answers

Please explain the intuition behind the dual problem in optimization.

How would you discover Stokes's theorem?

What are some examples of mathematics that had unintended useful applications much later?

Why does the fundamental theorem of calculus work?

Why is $A^TA$ invertible if $A$ has independent columns?

What is the Jacobian matrix?

Why do we use trig functions in Fourier transforms, and not other periodic functions?

Intuitive proof of multivariable changing of variables formula (Jacobian) without using mapping and/or measure theory?

Transpose of block matrix

What is integration by parts, really?

How to prove Lagrange multiplier theorem in a rigorous but intuitive way?

What are some mathematical topics that involve adding and multiplying pictures?

Does it make sense to learn mathematical concepts as you encounter them rather than in a fixed progression?

When has one sufficiently mastered an area of mathematics?

Intuition behind chain rule

Is there a mathematical notation of indexing a matrix?

How to physically interpret conjugate functions?

Why does the Cholesky decomposition requires a positive definite matrix?

Why must the gradient vector always be directed in an increasing direction?

How does Cramer's rule work?

Is basis change ever useful in practical linear algebra?

Intuition behind logarithm change of base

What are some interpretations of Von Neumann's quote?

Why is this allowed? ("Fourier's Trick"; finding the coefficients in a Fourier Series)

How to expand equation inside the L2-norm?

Mathematics - The big picture

Is there a mathematical notation for restricting the depth of a factorial?

Better Proofs Than Rudin's For The Inverse And Implicit Function Theorems

Why do we need to define Lebesgue spaces using equivalence classes?

Big list of "guided discovery" books