Tough Nuts to Crack

Tough Nuts to Crack

A Survey of Mathematical Problems

young-woman-looking-at-math-problem-on-blackboard_web

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

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

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

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

Sketching Graphs                        Solution


Problems on proofs:

Tough Nut to Crack I – Proofs

Proof by Induction        Solution


Problems on Series 

Tough Nut to Crack I – Series      Solution by Archie Morgan

Tough Nut to Crack Series II


Problems on Hyperbolic Functions 

Tough Nut to Crack I – Inverse hyperbolic function