Higher School Maths: Mathematician reminisces the HSC

Do you have what it takes to be a mathematician?
A theoretical physicist?
Can you rely on your mathematical foundations?

The subject of Calculus has long been considered a triumph of the human mind and many have sought to master it purely to prove to themselves that they can achieve it. Sometimes the beauty of Calculus and the part of it that is worthy of this reputation is lost among many mechanical manipulations because students struggle enough already with these and the subject becomes directed more towards familiarisation than toward understanding or mastery. Here I invite you to revisit high school maths with me from the point of view of a mathematician with a greater emphasis on conceptualisation, proof and rigour. The lasting impressions maths has created on me have always come from ideas, while the memorisations and manipulations tend to follow naturally as one spends time grappling with the subject. I want to share these inspiring ideas with you and how I came to understand them.

Learn how to investigate maths problems one step at a time to their natural conclusion and ultimately to think at a high level unassisted.

There are also numerous videos containing explanations as well as updates to help you get there.

This book is written with the Extension 2 student in mind and even the core Advanced and Extension 1 topics are expanded to an Extension 2 level, but every level of student should be able to gain something from this book, even if it is just to see what is out there mathematically.

Contents

• Introduction
• Chapter 1. Logic of proofs
• Chapter 2. Functions
• Chapter 3. Calculus of functions
• Chapter 4. Polynomial Functions
• Chapter 5. Trigonometric functions
• Chapter 6. Exponential and logarithmic functions
• Chapter 7. Solutions and comments
• Afterword and advice on taking exams
• Index
• Bibliography

About the Author

Dr Michael Sun did his HSC in 2004 achieving 99.95 and Dux of Normanhurst Boys High School. He won the University Medal at the University of Sydney, completing a B.Sc (advanced) with Honours obtaining High Distinctions in all Maths units (the highest grade). He also completed a M.Sc in Mathematics by research thesis and publication in record time at the University of Sydney in 2009. Dr Sun received his PhD in Mathematics from the University of Oregon finishing first in his class (Börsting Prize) and during his time there coauthored a paper which was accepted and published by the prestigious Communications in Mathematical Physics (2014). Dr. Sun returned to Sydney in 2017 after doing 2 years of pure maths research in Germany and China and travelling the world attending various maths conferences such as the International Congress of Mathematicians (ICM) and the Joint Meetings of the American Mathematical Society (JMAMS).