# Tough Nuts to Crack

### A Survey of Mathematical Problems

*You need to spend lots of time thinking about the problem. When I was young I had great difficulty in sleeping, so I spent lots of time thinking about mathematical problems instead of sleeping. It is very difficult to build up intuition. Somehow you need to spend time with the problems and I am not sure how to teach that.*

Karen Uhlenbeck

Mathematicians on Creativity by Peter Borwein

##### Carl De Boor (1937 – )

When, after some considerable, quite non-productive effort, usually while not at all consciously working on the problem, there appears, for no apparent reason, in your brain the answer to that problem.

Mathematicians on Creativity by Peter Borwein

##### Trigonometry Problems

#### Tough Nut to Crack Trigonometry Problem and Solution 1

Tough Nut to Crack on Trigonometry Fallacy

##### Problems on Diagonalising a Matrix

Diagonalising Matrices Question

The solution to Diagonalising Matrices

##### Challenging problems on Integration

Tough Nut to Crack _ Integration I

Integration I Singh Solution and Integration I Richards solution

Tough Nut to Crack II on Diff and Integration Solution

Tough Nut to Crack Integration III

Tough Nut to Crack III-Solution by Richards

Tough Nut to Crack Integration IV

Tough Nut to Crack – Integration V and Solution to Integration V

Tough Nut to Crack – Integration VI and Solution to Integration VI or alternative solution is Answer

Tough Nut To Crack – Improper Integral

Tough Nut to Crack – Integration Problem II

Tough Nut to Crack – 2015 Integration Problem

Tough Nut to Crack Integration and Area Problem

Tough Nut to Crack on a standard integral

Tough Nut to Crack on Integration Problem and Solutions by Beth Ing

##### Problems on Complex Numbers

Tough Nut to Crack-Complex Numbers I

Tough Nut to Crack – Complex Numbers II

##### Problems on Differentiation and its Applications

Differentiation Problem 1 Solution by Charlotte Dellow

Differentiation Problem II Solution by Michael Hibbs

Application of Differentiation

**Sketching Graphs**

Tough Nut to Crack-Sketching Graphs

##### Problems on proofs:

The solution to induction proof

##### Problems on Series

Tough Nut to Crack Series Problem Archie Morgan – Maths challenge final-1