Kuldeep Singh's Maths Website

Welcome to Kuldeep Singh's Maths Website

The first woman to win the Fields Medal:


I teach mathematics at the University of Hertfordshire. This web site covers mathematics up to 2nd year undergraduate studies and  I would appreciate any helpful comments regarding this site. Please send your comments via email to k.singh@herts.ac.uk

A film about Alan Turing - The Imitation Game; see the following link:



The only way to learn mathematics is to do mathematics. It is not a spectator sport and you must try as many exercises as possible to understand and digest mathematics. Enjoy your journey through this web site and good luck!

Online tests in mathematics are here

You may wonder how any mathematics gets done when one has to teach, advise students, serve on committees, referee papers, write letters of recommendation, interview prospective faculty. Well, I take long showers.

Mathematicians on Creativity by Peter Borwein

"Mathematics is essential for driving human progress and innovation in this century."  Mark Zuckerberg (Facebook Founder).

"Mathematics is the most fundamental of the sciences - the language they are all written in. The best mathematical minds benefit us all by expanding the sphere of human knowledge." Yuri Milner (Russian Tech Billionaire).

Women in mathematics

Mathematics is obviously something that women should be able to do very well. It's very intuitive. You don't need a lot of machinery, and you don't need a lot physical strength. You just need stamina, and women often have a great deal of stamina. 

Mary Ellen Rudin (1924 to 2013)

Hypatia of Alexandria being hacked to death for her mathematical discoveries in 415 AD.

dramatization of  Hypatia's story can be seen in the film Agora. A trialer of this is at the following url:


Women Mathematiciains biographies are here

Mathematics at the University of Hertfordshire

See Amy Washington disucss her time on the mathematics programme http://www.youtube.com/watch?v=WgE9ulN5egI

See Della Avery discuss her time on the mathematics programme https://www.youtube.com/watch?v=x3jn9XAqjD4

Mathematics at UH video

Sometimes when you work though an example, you suddenly get an insight which you wouldn’t have got if you’d just been working abstractly with the hypothesis of your future theorem. I guess both of these are obvious pieces of advice, but they are ignored more often than they should be … if the problem is worthwhile, give it a good try. Take months, maybe years if necessary, before announcing to the world, “This is as far as I can go. I’m quitting.” It is disgraceful to give up before you have given it a good college try.

Irving Kaplansky (1917 to 2006)

More Mathematical People by Albers

Some mathematicians are birds, others are frogs. Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details of particular objects, and they solve problems one at a time… Mathematics needs both birds and frogs. Mathematics is rich and beautiful because birds give it broad visions and frogs give it intricate details. Mathematics is both great art and important science, because it combines generality of the concepts with depth of structures. It is stupid to claim that birds are better than frogs because they see further, or that frogs are better than birds because they see deeper. The world of mathematics is both broad and deep, and we need birds and frogs working together to explore it.

Freeman Dyson 1923 - present

Notices of the American Mathematical Society Feb 2009

The one person who ignited my love for mathematics was Lakshman Sinnadurai, a University College London (UCL) graduate of 1961. Below is a bench dedicated to his memory. Sadly he passed away in 2005.

"You can always tell a Harvard man, but you can't tell him much".   (James Barnes 1866-1936).

My office hours are Monday 3 to 4pm and Tuesday 12 to 1pm.

My coffice hour is Tuesday 4 to 5pm in Starbucks in the Forum.  I will be waiting for you.

Qualities of a good mathematics student:

·         An ability to tackle problems that are not routine variations of textbook or exam questions

·         A sound understanding of mathematical logic, the concept of proof, and counter-example

·         A readiness to explore ideas beyond the confines of the syllabus

·         Knowing standard formulas – without needing a formula sheet

·         Having good numerical skills – without needing a calculator

·         Willing to spend time thinking about a problem whose solution is not immediately obvious

·         Having good geometric insight

·         Being good at algebraic manipulation

·         Knowing that geometry can be used to think of algebraic problems, and algebra can solve geometric problems

·         Able to construct logical proofs

·         Connecting apparently different areas of mathematics

·         Thinking flexibly and creatively

·         When faced with a difficult question that appears insoluble, to think of a simpler version of the problem, solve it, and then upgrade the solution to a solution of the original problem

·         After solving a problem, reflecting on its solution, thinking about finding a different solution relating the solution to other problems

·         Developing a good style in writing mathematics

·         Appreciating generalization and overall mathematical structures

·         Always being on the lookout for fallacious logic in arguments

·         Being interested in the history of mathematics

·         Working with their peers who have the same passion for mathematics, with a willingness to match their minds against others in a friendly rivalry

·         Reading popularisations of mathematics by authors such as Martin Gardner, Ian Stewart and John Barrow

The Mathematical Digest

Teaching for 2012-2013 Academic Year:

Linear Algebra

Number Theory

Mathematical Techniques 1

Real Analysis

Engineering Mathematics

Investigation in Mathematics

Teaching for 2013-2014 Academic Year:

Linear Algebra

Number Theory

Mathematical Techniques 1

Real Analysis

Engineering Mathematics

Investigation in Mathematics

Group Discussions can be found here: groups.google.com/forum/

Examination Preparation

How to lose marks in a maths exam by Gillian Stansfield and OU tutors