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

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

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 VI  and  Solution to Integration VI   or alternative solution is Answer

Tough Nut To Crack – Improper Integral

Tough Nut to Crack – Integration Problem II

Another Integration Problem

Tough Nut to Crack –  2015 Integration Problem

Tough Nut to Crack Integration and Area Problem

Tough Nut to Crack on a standard integral

Problems on Complex Numbers

Tough Nut to Crack-Complex Numbers I

Tough Nut to Crack – Complex Numbers II

Problems on Differentiation and its Applications

Application of Differentiation

Sketching Graphs

Tough Nut to Crack-Sketching Graphs

Problems on proofs:

Tough Nut to Crack I – Proofs

Induction Proof

The solution to induction proof

Problems on Hyperbolic Functions

Tough Nut to Crack I – Inverse hyperbolic function