**Videos of lectures are under Engineering Mathematics link.**

Photos of class interaction:

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# Learn mathematics online - Maths for all

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# Qualities of a good mathematics student:

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HELLO

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.

*The first woman to win the Fields Medal:*

*Studying mathematics at the University of
Hertfordshire:*

Maryam Mirzakhani, Iranian Mathematician, Fields Medal 2014, 1977-2014

*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!*

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)*

* 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).*

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

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. Here is a bench dedicated to his memory. Sadly he passed away in 2005.

- 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

**Videos of lectures are under Engineering Mathematics link.**

Photos of class interaction: