Course list
For a history of course offerings in each term, please visit HERE
Starting in Fall of 2024, the faculty of Applied Mathematics major will mostly follow the following (unofficial) course schedule indefinitely. The table should be self-explanatory. However, there are a few points about the alternating courses:
- Classes that are meant to alternate with each other, year by year, will be listed as
Course 1/Course 2. - Some courses are offered every other year and will be marked as
alternate.
Limited exceptions may happen due to different circumstances and will be communicated clearly, in advanced to the students via emails and official schedule sent out from Academic Affairs.
Students may use this for general course planning for their career at Fulbright.
| Fall | Spring |
|---|---|
| 100 level | 100 level |
| Calculus | Linear Algebra |
| Idea of Mathematics | Multivariable Calculus |
| Intro to Statistics (CORE) | Intro to Statistics (CORE) |
| 200 level | 200 level |
| Probability | Differential Equations |
| Numerical analysis (alternate) | Discrete Mathematics |
| Intro to Quantitative Finance | |
| 300 level | 300 level |
| Real Analysis / Abstract Algebra | Optimization/ Topology and Measure Theory |
| Stat learning / Mathematical Statistics | Operations Research (Special, limited offering) |
| Research seminar | |
| Stochastic Calculus (alternate) |
The following is the most updated list of courses currently offered by other majors that could be counted to fulfill the elective applied course requirements.
| Major | Courses |
|---|---|
| Computer Science | 302: Algorithm |
| 307: Introduction to Machine Learning | |
| 204: Introduction to AI | |
| Economics | 211: Game Theory |
| 212: Cost-Benefit Analysis | |
| 201: Microeconomics Analysis | |
| 203: Macroeconomics Analysis | |
| 209: Econometrics | |
| Engineering | 209: Signals, Systems, and Control |
| 301: Computer Vision | |
| Applied Mathematics | 204: Introduction to Quantitative Finance |
| 3xx: Operations Research | |
| 308: Statistical Learning |
NOTE: You cannot double count one course for both applied elective and other requirement.
MATH 101: Calculus
How can we estimate the weight of a bridge? What price should a store set for a product so as to maximize the revenue? Calculus provides tools to answer these questions and many more. Calculus is fundamental to many scientific disciplines including physics, engineering, statistics, computer science, and economics. Using everyday language and graphs, as well as equations, data, and numerical approaches, this course will provide the essential concepts of Calculus, illustrated, and explored through a wide range of real-world examples. Students will develop their critical thinking and problem-solving skills, while also gaining a solid preparation for higher-level courses such as differential equations or statistics. The main topics are functions, limits, derivatives, and integrals.
Pre-requisites: None
MATH 102: Ideas of Mathematics
Mathematics is more than computations and solving equations. Often, what excites math lovers isn’t just the answer to a particular problem but the ideas behind the explanations and how they lead to new insights and possibilities. At its best, mathematics contains all of the following: creativity, beauty and, of course, precision. A masterpiece in mathematics could be compared to a great drawing or a classic novel. As an example, Martin Hairer’s regularity structure is compared to Lord of the Rings on Quanta Magazine. The course will be a survey of some of the fundamental ideas in mathematics in the past two hundred years (possibly even more). It starts with the basic language of modern mathematics, logic and set theory. Then, depending on the interests and time, we will discuss about some (but not limited to) of the following topics: infinity, number theory, combinatorics, probability, game theory, linear algebra, discrete dynamical systems.
Pre-requisites: None
MATH 103: Linear Algebra
Have you ever wondered how Google search can find exactly what you need among billions of web pages? How can your smartphone recognize your face? How can an analyst handle thousands of survey results and draw the most significant conclusion? Linear Algebra provides the engines that power these applications. The objects and structures in Linear Algebra can be used in many areas, from physics to data mining or business analysis. This course is designed to help students understand the basic concepts and methods of Linear Algebra as well as how to build real-world models and compute solutions using computer programming (Matlab/Python). Major topics in this course include vectors and matrices, matrix operations, determinants, solving systems of linear equations, eigenvalues and eigenvectors, matrix decompositions, and real-life applications.
Pre-requisites: None
MATH 104: Multidimensional Calculus
How do we describe the trajectory of a space shuttle? How is the human body affected by scuba diving to different depths for different lengths of time? The mathematics required to describe most real life systems involves functions of more than one variable. The concepts of the derivative and integral from a first course in calculus must therefore be extended to higher dimensional settings. In this course students will be guided through the essential ideas of multivariable calculus, including partial derivatives, multiple integrals and vector calculus, and their applications. These mathematical tools are used extensively in the physical sciences and engineering, and in other areas including economics and computer graphics.
Pre-requisites: MATH 101
MATH 105: Introduction to Statistics
How do we know which Covid-19 vaccine is better? Which combination of policies could help promoting start-up companies? These questions could be answered with the help of Data analysis. Social scientists need to process survey results. Natural scientists want to analyze experiment’s outcomes. Modern statistical methods and state of the art computing software can help finding valuable information from a large and confusing data set. This course will provide students with basic statistics concepts and practical coding skill in Python. Students will be able to describe and find characteristic of the data, explore, and confirm relationship among data, and draw answer for questions from their own discipline via hand-on experience with various projects. Some main topics are data visualization, descriptive statistics, parameter estimation, parametric and non-parametric hypothesis testing, ANOVA.
Pre-requisites: None
Cross-list: Economics
MATH 201: Differential Equations
What is the math behind radioactive dating, where a radioactive substance can be used to estimate the ages of ancient objects? How long does it take to cool down a room by 5 degrees? Differential equations are the mathematical language to answer these questions. They are also the language to describe the laws of nature and many problems in science and engineering. This course is an introduction to ordinary differential equations (ODEs). In this course, students will learn basic concepts of differential equations and solution methods for different types of ODEs. Students will experience how ODEs are used to model simple real-life problems in Matlab, Octave, Mathematica, or Python. The covered topics include first and second-order equations, higher-order equations, and systems of equations.
Pre-requisites: MATH 101
MATH 202: Discrete Mathematics
How can Google maps find the fastest path for a trip between two locations? How can an admission system match applicants to the best suited university based on their preference and exam results? The answers to these questions arise from the study of Discrete Mathematics, which is a branch of Mathematics that deals with entities like integers, sets, graphs with distinct and separate values. The properties of discrete objects and structures play an essential role in many fields such as Theoretical Computer Science, Probability, Statistics and Cryptography. This course will provide basic knowledge of Combinatorics and Graph theory along with various methods of mathematical reasoning. Students will practice producing and writing formal rigorous proofs. Major topics in this course include set theory, Combinatorial counting methods, Graph theory (Eulerian walk, Hamiltonian cycle, Spanning Tree, Planar graph, etc.)
Pre-requisites: At least 1 100-level math class
MATH 203: Numerical Analysis
Numerical Analysis stands at the boundary of mathematics and computer science, offering essential tools and methodologies for solving complex mathematical problems through computational means. This course is designed as an introductory exploration into the world of computational mathematics, aiming to seamlessly connect the dots between the elegance of theoretical mathematics and its vast array of practical applications across diverse disciplines such as natural sciences, computer science, engineering, economics, and beyond. In this course, students will be introduced to the concepts of error, accuracy, convergence, complexity, and conditioning. The topics include solving nonlinear equations, systems of equations, solving least squares problems, and interpolation.
Pre-requisites: MATH 103, Basic Programming, MATH 101 is not required but highly recommeneded
MATH 204: Intro to Quantitative Finance
This course equips students with practical programming and mathematical skills necessary for addressing prevalent challenges in finance. These challenges include constructing effective personal finance plans, fair pricing of financial products, and the proficient use of risk management tools. Throughout the course, students will comprehend the formidable impact of compounded interests, witnessing the transformation of a small amount of money into a significantly larger sum over time. Additionally, students will acquire the skills to analyze stock prices and derive key investment performance metrics, such as stock returns and volatilities. The course delves into elucidating the correlation between the returns and volatilities of individual stocks and those within combined portfolios. Students are also trained to construct and manage investment portfolios wisely, aiming for good returns with acceptable risks. Furthermore, the curriculum introduces students to financial derivatives, including futures contracts and options, enabling them to hedge financial portfolios or even speculate on market movements. All these engaging topics are reinforced through practical case studies.
Pre-requisites: MATH 105
MATH 205: Probability
If a person gets a positive (Covid-19) test, then how likely he/she may get infected with Covid-19? What is the chance to win a lottery jackpot? Students can have precise answers after taking this course.
This course will provide students with basic foundation in probability theory which could be considered as a tool to perform inferential statistics. Students will be able to compute the probabilities for some particular events in different contexts or scenarios. Some main topics are basic concepts in probability, conditional probability, random variables, expected values, some common discrete and continuous probability distributions, jointly distributed random variables, sampling distributions and limit theorems.
Pre-requisites: MATH 101
MATH 301: Optimization
Optimization is a common problem in various fields, ranging from everyday decision-making to complex problem-solving in computer science, economics, science and engineering. What is the fastest path travelling from A to B? How is a model configured to best fit a given dataset? How to build an investment portfolio that maximizes returns while minimizing risks. How electricity is distributed in the network to ensure optimal power flow and minimize losses. All these questions can be answered by solving optimization problems. This course introduces the principles, techniques, and applications of optimization, a fundamental concept that involves finding the best possible solution from a set of alternatives. It is a blend of applied mathematics and computer science. However, it also benefits students majoring in economics, engineering, and integrated science, particularly those with an interest in computational topics.
Pre-requisites: MATH 101, MATH 103, Basic Programming Skills
Cross-list: CS
MATH 305: Stochastic Calculus
Many business or financial processes are occurring randomly every moment, but business managers or investors need to monitor them constantly as well as predict their future short-term and long-term movements to propose appropriate action plans. For instance, stock investors always want to update their current stock values as well as the future stock price movement directions. Sale managers also want to predict the number of customers buying their products next months for better business plans. This course aims to equip students’ knowledge and skills to meet such business demands. In particular, students learn about properties of different random processes, how to model some random phenomena by suitable random processes and how to simulate possible future movements of the phenomena. Several case studies are presented in the course so that student can learn and practice to solve business problems. This course also offers a strong foundation for further advanced applications on financial derivative pricing, portfolio optimization.
Pre-requisites: MATH 205
Cross-list: ECON
MATH 302: Abstract Algebra
Abstract Algebra is a cornerstone of Modern Mathematics. It deals with some of the most abstract structures and operations. The course will provide some basic foundation of group theory (cyclic group, permutation group, group action,…) and some fundamental theorems such as Lagrange and Sylow theorems.
Pre-requisite: MATH 103
MATH 306: Financial Mathematics
Do you want to be financial independence after 20-30 working years? If so, you should have a financial plan for regularly saving and investing a part of your income to grow your wealth. This course will help you build such a financial plan. Through the course, you will sense the amazing power of compounded interests in accumulating a small amount of money to a much bigger one over time. In addition, you will learn how to build and manage your investment portfolios wisely to obtain good returns with acceptable risks. Furthermore, you are introduced to financial derivatives such as future contracts and options to hedge your portfolios or even speculate your market predictions. All the above interesting contents are trained and practiced through practical case studies. This course also offers a strong foundation for further advanced applications such as financial derivative pricing, portfolio optimization.
Pre-requisites: MATH 205
Cross-list: ECON
MATH 307: Real Analysis
What is a real number? Why are there “more” real numbers than rational numbers when both sets of numbers are infinite? If a sequence does not blow up to infinity, does this mean that it must eventually converge? Is there a function that is continuous everywhere but nowhere differentiable? What is the relationship between continuity and integrability? Real Analysis answers these questions and many more. This course revisits familiar topics, such as real numbers, sequences, series, topology in the real line, limits, continuity, and integrals, but studies them in a mathematically rigorous way. It can be the first exposure of students to abstract mathematics, where graphical, numerical, and intuitive arguments are replaced by rigorous mathematical proofs.
Pre-requisites: MATH 101
MATH 308: Statistical Learning
Machine learning (ML) has enjoyed tremendous successes in a wide variety of applications. Most notable are computer vision and natural language processing. Those accomplishments are thanks to its solid foundations in statistics, computer science and mathematics. The next frontier for ML is business and/or finance where ML’s applications are in an early stage. Successful ML integrations into business domain require a rigorous understanding of the foundations of ML so that appropriate models can be adapted to real-world applications with a careful consideration of costs and risks involved. This statistical learning course takes you on a journey from classical statistics to statistical learning theory. You will start with basic ideas originated from statistics, understand the strengths and weaknesses of classical models and develop the learning algorithms addressing those weaknesses. The course will build you a strong background to move on to the next stage in ML with more advanced courses or to create real-world applications.
Pre-requisites: MATH 101, MATH 103, MATH 205
Cross-list: CS
MATH 310: Mathematical Statistics
This course provides the rigorous mathematical foundation for statistics. Designed for students who already know how to conduct standard hypothesis testings, the course will give a logical explanation for the universality of the normal distribution and why the normal distribution plays the central role in most hypothesis tests. The students will understand why the tools they learned in previous statistics courses work. Furthermore, built from the foundation of probability, the course will also discuss rigorously the theory of some of the important ideas in statistics such as parametric/nonparametric estimation, point estimation, Bayesian inference, linear regression, logistic regression, method of moments, maximum likelihood.
Pre-requisites: MATH 205, MATH 104
MATH 311: Mathematics Research Seminar
This is a research seminar aimed at students who wish to major in mathematics. In this course, mathematics faculty will first take turns presenting research problems in their respective fields of expertise. The goal is to expose students to different lines of research in mathematics so that interested students may choose a potential topic to explore for Senior Capstone. After the faculty’s presentations, students will present assigned readings. The goal of this part is to help students learn how to synthesize and convey ideas of other peoples’ work. Along the way, students will learn how to apply learned mathematical concepts to understand complex research topics.
Pre-requisites: At least 1 300-level course