## Todai Entrance Exam: Math 2017 – Problem 2

(1)             (2)     Let and . So, thanks to the given fact:     (3)         We solve the characteristic equation of the above homogenous second order linear differential equations:     So:     If :     which is the excluded solution. If [...]

## Todai Entrance Exam: Math 2019 – Problem 2

(1) Let , so :     (2) (i) From Eq. (2.1), we have:     Remember that:     So:                 Notice that:     So:         Working… (ii) I speculate the general form of the solution is: . Eq. (2.3) implies that:   [...]

## Todai Entrance Exam: Math 2018 – Problem 2

Problem link (1) Base case: Show that holds true. We have: . Induction step: Show that holds true leads to the fact that holds true.         So the statement follows. (2) This problem is interestingly tricky. First we find the critical points of :     If then (due to the fact [...]

## [Notes] Cracking the GRE Mathematics Subject Test – Steve Leduc

Page 172: http://farside.ph.utexas.edu/teaching/sm1/lectures/node36.html#e4.32

## An intuition to an tangent plane to a surface

To me: Page 126 of Cracking the GRE Math Subject Test. A rigorous proof can be found here (Calculus, Howard Anton). A note of stress should be on “any smooth curve C on the surface”. Below is my attempt interpretation before looking at any proofs. While it cannot be considered as a proof, it shows [...]

## Entropy 2016, bảng A

It took me quite a lot of time to understand the question, though. I do not post the test here as I am not sure if I am permitted to do that. This post serves for my personal use. Even though the original questions are written in Vietnamese, I will be writing my solutions in [...]

## Triplet Loss’ derivative of VGG Face

We starts with the formula (1) of the paper.     We have:             By chain rule, we have:     We also have: – the th element of .   – the th element of . So:

## Learning From Data – A Short Course: Problem 8.6

Show that is minimized at .             Now we need to check what type of the found critical point is:     So the found critical point is the global minimum.

## Proof for Softmax Regression gradient

The notation of this proof comes from the article Softmax Regression by UFLDL Tutorial.     We have:       When :                                 When :                             Now we look carefully at the [...]