Advanced Mathematics (2235.YR.015722.1)
General information
Type: |
OBL |
Curs: |
1 |
Period: |
S semester |
ECTS Credits: |
6 ECTS |
Teaching Staff:
Prerequisites
Students should have successfully completed the course on "Applied Mathematics for Management"
COURSE CONTRIBUTION TO PROGRAM
This is a course that aims to introduce students to advanced topics in mathematics for Artificial Intelligence. It covers discrete mathematics, advanced linear algebra, approximation methods and advanced calculus. It is strongly motivated by applications in data analytics, cryptography and finance, and focuses on using mathematical software for practical problem solving. It will further develop and solidify the connections between concepts that students have previously learned in their introductory Applied Mathematics for Management course. It will prepare students for future study in the fields of data science, machine learning, cryptography and quantitative finance.
Course Learning Objectives
After completing this course, students will be able to:
- Apply a wide variety of advanced mathematical concepts including modular arithmetic, vector spaces and bases, series, numerical approximations of functions, and differential equations.
- Connect advanced mathematical methods to concepts and problems in data analytics, cryptography and finance.
- Fluently use mathematical software as part of day-to-day problem solving.
CONTENT
1. Discrete Mathematics Topics:
- Modular Arithmetic
- Introduction to Cryptography |
2. Advanced Algebra Topics:
- Vector Spaces
- Orthonormal Bases
- Numerical Linear Algebra |
3. Approximation Methods Topics:
- Series
- Numerical Analysis
- Numerical Optimization |
4. Advanced Calculus Topics:
- Ordinary Differential Equations
- Partial Differential Equations |
Methodology
The mathematical content of the course will be strongly motivated by and supplemented with relevant examples and applications including, but not limited to: public key cryptography; least squares regression; probability density functions used in statistics; the gradient descent method used in machine learning; differential equations in economics, including the Solow-Swan model of economic growth; option pricing models used in finance, including the Black-Scholes partial differential equation.
Mathematical software will be used ubiquitously to solve problems throughout this course.
Assessment criteria
The evaluation activities contributing to the final grade for this course will include two exams, continuous individual assessments, class participation and group work, and a peer evaluation.
Bibliography
Useful textbooks with applications pertinent to the course material include the following:
- William J. Gilbert and Scott A. Vanstone. "Introduction to Mathematical Thinking: Algebra and Number Systems". Pearson, 2004.
- Daniel Norman and Dan Wolczuk. "An Introduction to Linear Algebra for Science and Engineering" (3rd edition). Pearson, 2019.
- Richard L. Burden, Douglas J. Faires and Annette M. Burden. "Numerical Analysis" (10th edition). Cengage Learning, 2015.
- Knut Sydsaeter, Peter Hammond, Atle Seierstad and Arne Strom. "Further Mathematics for Economic Analysis" (2nd ed.). Pearson, 2008.
