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Course Criteria
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3.00 Credits
Probability theory is the foundation on which statistical data analysis depends. This course together with its sequel, Mathematics 215, covers topics in mathematical statistics. Both courses are recommended for math majors with an interest in applied mathematics and for students in other disciplines, such as psychology and economics, who wish to learn about some of the mathematical theory underlying the methodology used in their fields. Prerequisite(s): Mathematics 106. Not open to students who have received credit for Mathematics 314. [Q] Staff.
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3.00 Credits
The sequel to Mathematics 214. This course covers estimation theory and hypothesis testing. Prerequisite(s): Mathematics 214. Not open to students who have received credit for Mathematics 315. [Q] Staff.
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3.00 Credits
A differential equation is a relationship between a function and its derivatives. Many real-world situations can be modeled using these relationships. This course is a blend of the mathematical theory behind differential equations and their applications. The emphasis is on first- and second-order linear equations. Topics include existence and uniqueness of solutions, power series solutions, numerical methods, and applications such as population modeling and mechanical vibrations. Prerequisite(s): Mathematics 206. [Q] Normally offered every year. M. Greer.
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3.00 Credits
Mathematical modeling is a tool used by natural and social scientists, including physicists, biologists, engineers, economists, and political scientists. Mathematical models use the language of mathematics to describe and analyze complex systems. They extract the essential features of real world phenomena and represent the system in one or more mathematical forms. These abstract structures may include differential equations, dynamical systems, statistical models,and game-theoretic models, among others. Normally offered every year.
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3.00 Credits
Often, analyzing complex situations (like the weather, a traffic flow pattern, or an ecological system) is necessary to predict the effect of some action. The purpose of this course is to provide experience in the process of using mathematics to model real-life situations. The first half examines and critiques specific examples of the modeling process from various fields. During the second half each student creates, evaluates, refines, and presents a mathematical model from a field of his or her own choosing. Prerequisite(s): Mathematics 206. Not open to students who have received credit for Mathematics 341. Staff.
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3.00 Credits
The power and utility of mathematical modeling in the physical sciences is well recognized. What is less well-known is that mathematics can also be used to model social dilemmas-situations where the public good is in conflict with individual self-interest. The social dynamics involved in this so-called "tragedy of the commons" are analyzed using a branch of mathematics called game theory. In this course, students create models using classical and evolutionary game theory to gain insight into questions about how cooperation evolves, what is necessary for it to gain a foothold in a group, and under what conditions it will persist. Prerequisite(s): Mathematics 105. Enrollment limited to 30. B. Shulman.
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3.00 Credits
With varying subject matter, this seminar addresses both the oral and written communication of mathematics. The seminar focuses on understanding why rigor is necessary and what constitutes effective communication of mathematical ideas to different audiences. Students practice peer editing and peer reviewing, and learn how to write effective grant and thesis proposals. Prerequisite(s): Mathematics s21. Normally offered every year.
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3.00 Credits
An introduction to the foundations of mathematical analysis, this course presents a rigorous treatment of fundamental concepts such as limits, continuity, differentiation, and integration. Elements of the topology of the real numbers are also covered. Prerequisite(s): Mathematics 206 and s21. Normally offered every year. P. Jayawant.
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3.00 Credits
This course extends the concepts of calculus to deal with functions whose variables and values are complex numbers. Instead of producing new complications, this leads to a theory that is not only more aesthetically pleasing, but is also more powerful. The course should be valuable to those interested in pure mathematics, as well as those who need additional computational tools for physics or engineering. Topics include the geometry of complex numbers, differentiation and integration, representation of functions by integrals and power series, and the calculus of residues. Prerequisite(s): Mathematics 206. Staff.
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3.00 Credits
An introduction to basic algebraic structures common throughout mathematics. These include the integers and their arithmetic, modular arithmetic, rings, polynomial rings, ideals, quotient rings, fields, and groups. Prerequisite(s): Mathematics 205 and s21. Normally offered every year. D. Haines.
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