This course is designed to enhance students' mathematical ability, and equip them with the basic knowledge and skills of stochastic calculus for financial applications. Students will be introduced to stochastic processes, Brownian motion, and Ito calculus. Student will learn how to use quantitative analysis to derive the Black-Scholes formula for various types of options (European options, etc.). At the end of this course, students will be able to price various types of options and construct hedging strategies. The course also aims to develop students' creative and innovative abilities through various assessment tasks that involve the discovery and innovative process. Classes will encourage students to develop their discovery abilities through problem solving and class discussions. Stress will also be placed on common pricing and hedging problems in global financial markets to help students to discover the basic knowledge in the finance industry. Assignments will require students to discover and innovate through the use of mathematical concepts. Students will get to know how to use these theories to come up with their own analyses on different financial products. The final exam which covers topics discussed in the lectures will reveal the students' accomplishments in discovery and innovation.