# Author Archives: tomcircle

# Integral of x^x from 0 to 1

Recall: Gamma function

# What is Riemann’s Hypothesis ?

［中文］历史 History:

**Sir Atiyah Proof on 2018 September : (5 Pages PDF download here**)

https://drive.google.com/file/d/17NBICP6OcUSucrXKNWvzLmrQpfUrEKuY/view

**Bigger Lecture Notes video** (at 34 mins, inspired in Singapore)

Analytic function: preserve angle after transformation

# WiFi Password = Integral Answer

China 南京航空航天大学 Nanjing University of Aeronautics and Astronautics set the WiFi password as the answer of this integral (first 6 digits).

Can you solve it?

*(If can’t, please revise GCE “A-level” / Baccalaureate / 高考 Calculus* *微积分*)

**Answer** : Break the integral (I) into 2 parts:

I = A(x) + B(x)

**A(x) = – A(-x) => Odd function **

=> **A(x) = 0** since its area canceled out over [-2, 2]

**B(x) = B(-x) => Even function**

Let x = 2 sin t => dx = 2 cos t. dt

x = 2 = 2 sin t => sin t = 1 =>

t =π/ 2x = 0 = 2 sin t => sin t = 0 =>

t = 0

A smarter method using Analytic Geometry: A circle of radius 2 is

# Category Theory III Part 3

**3.1 Adjunction and Monad**

Tip:

L = Free,

R = Conservative (get rid of structure / forgetful)

Examples

L: C- >D

Monoid – > Free Monoid

Algebras – > Free Algebras…

R: D – > C

**Adjunction gives “Monad” **

**3.2 Monad Algebras**

Tip: Think Monad as “List” container

# [Quora] Common Core Math

Why did the approach to mathematics change with Common Core, rather than providing more structure to how it was previously taught? by Peter Kruger

# Spot The Mistake?

Solve:

Since the exponents (3+x) on both sides are equal,

=> 2 = 3