Basic notions of financial mathematics that the students should learn in a first course:

- Arbitrage theorem (also called the fundamental theorem of financial mathematics)
- Interest (different ways to calculate interest rates; general term structure of interest rates)
- Non-arbitrage principle, martingale (risk-neutral) measures
- Financial engineering products: forwards, futures, options, swaps, … why are they created, what are their uses, and their basic properties
- Stochastic calculus (stochastic differential equation, Ito integral, Ito lemma)
- Black-Scholes and some other derivatives pricing models
- Risk (why risk management is important; measures of risk; hedging)
- Elements of portfolio management / asset allocation

Recommended texts for a first course on financial mathematics:

- Buchanan – An undergraduate introduction to financial mathematics – 2006. (As the title indicates, this book is well suited for undergraduate students)
- Capinski and Zastawniak – Mathematics for finance: an introduction to financial engineering – 2004
- Chourdakis – Financial engineering: a brief introduction using the Matlab system – 2008 (Matlab is one of the best computer software for doing finance)
- Elliott and Kopp – Mathematics of financial markets, 2nd ed. – 2005
- Focardi and Fabozzi – The mathematics of financial modeling and investment management – 2004
- Harrison and Waldron – Mathematical economics and finance – 1998 (A rather elementary book, which also explains basic mathematical concepts such as linear algebra and elementray probability theory).
- Hull – Options, futures, and other derivatives, 5th ed. (A rather comprehensive introduction to derivatives, which is still accessible to undergraduate students)
- Lin – Lecture notes in mathematical finance – 1996 (This text is very mathematically-oriented)
- Neftci – Principles of financial engineering, 2nd ed. – 2008 (a very good book with many real-world examples)
- Pliska – Introduction to mathematical finance: discrete time models – 2001
- Ross – An introduction to mathematical finance – 1999
- Wilmott et al. – The mathematics of financial derivatives: a student introduction – 1996.

For Vietnamese students: I’m currently writing a textbook in Vietnamese, which will be available soon.