Undergraduate Level Math Book Recommendations

Originally posted on Singapore Maths Tuition:

Highly Recommended Math Books for University Self Study

Recently, a viewer of my website asked if I was able to suggest any undergraduate level university textbooks for self study that follows the university curriculum at NUS (National University of Singapore).

Self-study is challenging but not impossible. Choosing a good and appropriate book of the right level is of crucial importance. For instance, for beginners to Calculus, I wouldn’t recommend Principles of Mathematical Analysis (International Series in Pure and Applied Mathematics) by Rudin. It is simply too difficult for beginners or even intermediate students. Any book by Bourbaki is also not suitable for beginners, for instance.

I would like to suggest the following books (mainly for Pure Mathematics). Ideally, the motivated student is able to self study and obtain the knowledge equivalent to a 4 Year course at a university.

The recommendations are divided into Year 1, Year 2, Year…

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French & German’s Secondary School Maths Comparison

A French math teacher’s insight in math classes in Germany (15 years old = Secondary 3) and France (16/17 years old in Sec 4 & Pre-U / JC 1):

The French Math is more theoretical while the German Math (like English Math) is applied. So the result is Germany produces excellent precision engineers with Applied Math, while France produces 1/3 of the World’s Fields Medalists in theoretical Pure Math.

Many English GCE A-level top Math students from Singapore studying in French Universities face the same dilemma: while their French Math professors think they are “weak” in Math (i.e. French abstract Pure Math), yet they beat the French classmates in Applied Math.

The ideal Math Education is to have the best of both worlds: the Applied Math used in science & engineering, and the theoretical Pure Math in its powerful generalisation capability for higher research & development.

Love Math Graphs!

Originally posted on Singapore Maths Tuition:

How to remember graphs?

Many students have a hard time remembering how graphs look like.

Here is a humorous cartoon (suitable for Valentine’s Day) on how some graphs look like!

Remember, Maths is not just about exams, homework, or getting A1/A2. Maths, above all, is about the LOVE of learning and thinking.

math graphs

Featured book:
Love and Math: The Heart of Hidden Reality A New York Times Science Bestseller

What if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren’t even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry.

In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we’ve never seen, suffused with all the beauty…

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