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18.642 | Fall 2024 | Undergraduate

# Topics in Mathematics with Applications in Finance

### Lecture 1

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Video description: This video provides an introductory overview of a course combining mathematical theory and real-world financial applications, featuring lectures by academics and industry experts. The instructors emphasize the practical use of mathematics in finance, covering topics like bond math, portfolio optimization, and machine learning, while utilizing tools such as RStudio Cloud for data analysis. Additionally, the course includes guest speakers from prominent financial institutions, offering students exposure to cutting-edge quantitative finance concepts and industry practices.

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Video description: In this video Jake Xia provides an overview of key financial concepts, including market structure, types of financial products like stocks, bonds, derivatives, and the roles of various market participants. He also introduces investment strategies, emphasizing the importance of understanding personal financial goals, risk management, and the use of mathematical models in pricing and trading, culminating in a practical trading game to apply these concepts.

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Video description: This segment by Vasily Strela provides an explanation of interest rates, bonds, and their fundamental role in finance. It covers key concepts such as compound interest, discounting future cash flows, zero-coupon and coupon bonds, and the inverse relationship between bond prices and yields. The discussion also explores yield curves, their historical shapes, and how they can signal economic recessions, emphasizing the importance of understanding bond price sensitivities through measures like duration and convexity for effective fixed-income investing.

Introduction. Financial Terms and Concepts. Bond Math Slides (PDF)

Using R/R Studio to Analyze Financial Time Series (PDF)

R Studio Files (ZIP)

Read About the Investment Game

## Course Info

##### Instructors

- Dr. Peter Kempthorne
- Dr. Vasily Strela
- Dr. Jake Xia

##### Departments

- Mathematics

##### As Taught In

Fall 2024

##### Level

Undergraduate

##### Topics

- Business
  - Finance
- Mathematics
  - Applied Mathematics
  - Probability and Statistics

##### Learning Resource Types

notes Lecture Notes
theaters Lecture Videos
assignment Problem Sets
assignment Activity Assignments
group_work Projects
Readings

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