Undergraduate Course Descriptions

MATHUA 009 Algebra, Trigonometry, and Functions
4 points. Fall, Spring and Summer terms. Course homepage.
Prerequisites:
High school math or permission of the department.
Description:
This course serves as preparation for MATHUA 120 Discrete Mathematics, MATHUA 121 Calculus I, MATHUA 131 Mathematics for Economics I, and MATHUA 140 Linear Algebra. Topics include: intermediate algebra and trigonometry; algebraic, exponential, logarithmic, and trigonometric functions and their graphs.
This course was formerly titled "Precalculus" and then "Algebra and Calculus". The course title was last updated to "Algebra, Trigonometry and Functions" for the start of the Fall 2022 semester. 
MATHUA 120 Discrete Mathematics
4 points. Fall, Spring and Summer terms. Course homepage.
Prerequisites:
At least one (1) of the following prerequisites:
 Completion of MATHUA 009 Algebra, Trigonometry and Functions with a grade of C or higher
 SAT score of 670 or higher on mathematics portion
 ACT/ACTE Math score of 30 or higher
 Valid AP Score:
 AP Precalculus score of 4 or higher
 AP Calculus AB score of 3 or higher
 AP Calculus BC score of 3 or higher
 A Level Maths score of C or higher
 Students who took A Level Further Maths should contact the Math Department
 AS Level Maths score of B or higher
 IB Mathematics exam result from 2021  2027
 IB Analysis and Approaches HL score of 5 or higher
 IB Applications and Interpretations HL score of 5 or higher
 IB Analysis and Approaches SL score of 7
 IB Mathematics exam result from 2014  2020
 IB Mathematics HL score of 5 or higher
 IB Mathematics SL score of 6 or higher
 IB Mathematical Studies SL score of 7
 Passing Calculus/MFE I placement exam
Description:
This course is a onesemester introduction to discrete mathematics with an emphasis on the understanding, composition and critiquing of mathematical proofs. At the semester's conclusion, the successful student will be able to:
 write clear mathematical statements using standard notation and terminology.
 understand and execute a variety of proof techniques (contradiction, induction, etc.).
 show fluency in the language of basic set theory and Boolean logic.
 understand the basic theorems and their implications in a variety of (discrete) fields including:
 function theory
 group theory
 number theory
 graph theory

MATHUA 121 Calculus I
4 points. Fall, Spring and Summer terms. Course homepage.
Prerequisites:
At least one (1) of the following prerequisites:
 Completion of MATHUA 009 Algebra, Trigonometry and Functions with a grade of C or higher
 SAT score of 670 or higher on mathematics portion
 ACT/ACTE Math score of 30 or higher
 Valid AP Score:
 AP Precalculus score of 4 or higher
 AP Calculus AB score of 3 or higher
 AP Calculus BC score of 3 or higher
 A Level Maths score of C or higher
 Students who took A Level Further Maths should contact the Math Department
 AS Level Maths score of B or higher
 IB Mathematics exam result from 2021  2027
 IB Analysis and Approaches HL score of 5 or higher
 IB Applications and Interpretations HL score of 5 or higher
 IB Analysis and Approaches SL score of 7
 IB Mathematics exam result from 2014  2020
 IB Mathematics HL score of 5 or higher
 IB Mathematics SL score of 6 or higher
 IB Mathematical Studies SL score of 7
 Passing Calculus/MFE I placement exam
Description:
Derivatives, antiderivatives, and integrals of functions of one real variable. Trigonometric, inverse trigonometric, logarithmic and exponential functions. Applications, including graphing, maximizing and minimizing functions. Areas and volumes.
Note: Students cannot mixandmatch, combine, or doublecount between the Calculus and Math for Economics sequences. Switching back and forth between the Calculus and Math for Economics sequences is not permitted. Students may count only the Calculus sequence or only the Math for Economics sequence towards their degree requirements.

MATHUA 122 Calculus II
4 points. Fall, Spring and Summer terms. Course homepage.
Prerequisites:
At least one (1) of the following prerequisites:
 Passing MATHUA 121 Calculus I with a grade of C or better
 Valid AP score:
 AP Calculus AB score of 4 or higher
 AP Calculus BC score of 4 or higher
 A Level Maths score of B or higher
 Students who took A Level Further Maths should contact the Math Department
 IB Mathematics exam result from 2021  2027
 IB Analysis and Approaches HL score of 6 or higher
 IB Applications and Interpretations HL score of 6 or higher
 IB Mathematics exam result from 2014  2020
 IB Mathematics HL score of 6 or higher
 Passing Calculus II placement exam
Description:
Techniques of integration. Further applications. Plane analytic geometry. Polar coordinates and parametric equations. Infinite series, including power series.
Note: Students cannot mixandmatch, combine, or doublecount between the Calculus and Math for Economics sequences. Switching back and forth between the Calculus and Math for Economics sequences is not permitted. Students may count only the Calculus sequence or only the Math for Economics sequence towards their degree requirements. The Math Department encourages students and advisors to contact us first if there are any questions regarding which sequence a student should register for.

MATHUA 123 Calculus III
4 points. Fall, Spring and Summer terms. Course homepage.
Prerequisites:
At least one (1) of the following prerequisites:
 Passing MATHUA 122 Calculus II with a grade of C or higher
 AP Calculus BC score of 5
 IB Mathematics exam result from 2021  2027
 Analysis and Approaches HL score of 7
 IB Mathematics exam result from 2014  2020
 Further Mathematics HL score of 6 or higher
 Passing Calculus III placement exam
Description:
Functions of several variables. Vectors in the plane and space. Partial derivatives with applications, especially Lagrange multipliers. Double and triple integrals. Spherical and cylindrical coordinates. Surface and line integrals. Divergence, gradient, and curl. Theorem of Gauss and Stokes.
Students cannot take both MATHUA 123 and MATHUA 129.
Note: ^{ }Students cannot mixandmatch, combine, or doublecount between the Calculus and Math for Economics sequences. Switching back and forth between the Calculus and Math for Economics sequences is not permitted. Students may count only the Calculus sequence or only the Math for Economics sequence towards their degree requirements. The Math Department encourages students and advisors to contact us first if there are any questions regarding which sequence a student should register for.

MATHUA 129 Honors Calculus III
4 points. Fall and Spring terms. Course homepage.
Prerequisites:
At least one (1) of the following prerequisites:
 Passing MATHUA 122 Calculus II with a grade of A or higher
 A grade of "Pass/Fail" or an "Incomplete" do NOT satisfy the prerequisite
 AP Calculus BC score of 5
 IB Mathematics exam result from 2021  2027
 Analysis and Approaches HL score of 7
 IB Mathematics exam result from 2014  2020
 Further Mathematics HL score of 6 or higher
 Passing Calculus III placement exam
Note: Students who took an A Level Further Maths exam should contact the Math Department with a copy of their official exam score report. The student's name and exam scores must be clearly visible.
Description:
Similar to MATHUA 123 Calculus III, but at a faster pace and deeper level. Functions of several variables. Vectors in the plane and space. Partial derivatives with applications, especially Lagrange multipliers. Double and triple integrals. Spherical and cylindrical coordinates. Surface and line integrals. Divergence, gradient, and curl. Theorem of Gauss and Stokes. Students interested in an honors mathematics degree especially encouraged to consider this course.
Students cannot take both MATHUA 123 and MATHUA 129.
Note: Students cannot mixandmatch, combine, or doublecount between the Calculus and Math for Economics sequences. Switching back and forth between the Calculus and Math for Economics sequences is not permitted. Students may count only the Calculus sequence or only the Math for Economics sequence towards their degree requirements. The Math Department encourages students and advisors to contact us first if there are any questions regarding which sequence a student should register for.
 Passing MATHUA 122 Calculus II with a grade of A or higher

MATHUA 131 Math For Economics I
4 points. Fall, Spring and Summer terms. Course homepage.
Prerequisites:
At least one (1) of the following prerequisites:
 Completion of MATHUA 009 Algebra, Trigonometry and Functions with a grade of C or higher
 SAT score of 670 or higher on mathematics portion
 ACT/ACTE Math score of 30 or higher
 Valid AP Score:
 AP Precalculus score of 4 or higher
 AP Calculus AB score of 3 or higher
 AP Calculus BC score of 3 or higher
 A Level Maths score of C or higher
 Students who took A Level Further Maths should contact the Math Department
 AS Level Maths score of B or higher
 IB Mathematics exam result from 2021  2027
 IB Analysis and Approaches HL score of 5 or higher
 IB Applications and Interpretations HL score of 5 or higher
 IB Analysis and Approaches SL score of 7
 IB Mathematics exam result from 2014  2020
 IB Mathematics HL score of 5 or higher
 IB Mathematics SL score of 6 or higher
 IB Mathematical Studies SL score of 7
 Passing Calculus/MFE I placement exam
Description:
This course is only open to Economics Majors and prospective Economics Majors. If an Economics Major decides to double or joint major in Math, the Math for Economics sequence of courses will replace the Calculus requirement.
Elements of calculus and linear algebra are important to the study of economics. This class is designed to provide the appropriate tools for study in the policy concentration. Examples and motivation are drawn from important topics in economics. Topics covered include derivatives of functions of one and several variables; interpretations of the derivatives; convexity; constrained and unconstrained optimization; series, including geometric and Taylor series; ordinary differential equations; matrix algebra; eigenvalues; and (possibly) dynamic optimization and multivariable integration.
Note: Students cannot mixandmatch, combine, or doublecount between the Calculus and Math for Economics sequences. Switching back and forth between the Calculus and Math for Economics sequences is not permitted. Students may count only the Calculus sequence or only the Math for Economics sequence towards their degree requirements. The Math Department encourages students and advisors to contact us first if there are any questions regarding which sequence a student should register for.
This course was formerly numbered MATHUA 211. The course number was updated to MATHUA 131 for the start of the Fall 2022 semester. The course content remains the same, only the course number has changed.

MATHUA 132 Math For Economics II
4 points. Fall, Spring and Summer terms. Course homepage.
Prerequisites:
At least one (1) of the following prerequisites:
 Completion of MATHUA 131 Math for Economics I with a grade of C or higher
 Passing Math for Economics II placement exam
Description:
This course is only open to Economics Majors and prospective Economics Majors. If an Economics Major decides to double or joint major in Math, the Math for Economics sequence of courses will replace the Calculus requirement.
By the end of Math for Economics II, students should have a complete understanding of optimization and should be able to apply the Lagrange multipliers approach to constrained optimization problems. They will also learn to solve systems of equations using linear algebra. Time permitting, they will also be exposed to the principal methods of dynamic analysis of economic processes, and introductory concepts and results of integration and differential equations. A student should be able to find solutions of elementary differential equations and analyze their stability.
Note: Students cannot mixandmatch, combine, or doublecount between the Calculus and Math for Economics sequences. Switching back and forth between the Calculus and Math for Economics sequences is not permitted. Students may count only the Calculus sequence or only the Math for Economics sequence towards their degree requirements. The Math Department encourages students and advisors to contact us first if there are any questions regarding which sequence a student should register for.
This course was formerly numbered MATHUA 212. The course number was updated to MATHUA 132 for the start of the Fall 2022 semester. The course content remains the same, only the course number has changed.

MATHUA 133 Math For Economics III
4 points. Fall and Spring terms. Course homepage.
Prerequisites:
At least one (1) of the following prerequisites:
 Completion of MATHUA 132 Math for Economics II with a grade of C or higher
 A grade of "Pass/Fail" or an "Incomplete" do NOT satisfy the prerequisite
 Passing Math for Economics III placement exam
Description:
This course is only open to Economics Majors and prospective Economics Majors. If an Economics Major decides to double or joint major in Math, the Math for Economics sequence of courses will replace the Calculus requirement.
Further topics in vector calculus. Vector spaces, matrix analysis. Linear and nonlinear programming with applications to game theory. This course will provide economics students who have taken MATHUA 131 Mathematics for Economics I and MATHUA 132 Mathematics for Economics II with the tools to take higherlivel mathematics courses.
Note: Students cannot mixandmatch, combine, or doublecount between the Calculus and Math for Economics sequences. Switching back and forth between the Calculus and Math for Economics sequences is not permitted. Students may count only the Calculus sequence or only the Math for Economics sequence towards their degree requirements. The Math Department encourages students and advisors to contact us first if there are any questions regarding which sequence a student should register for.
This course was formerly numbered MATHUA 213. The course number was updated to MATHUA 133 for the start of the Fall 2022 semester. The course content remains the same, only the course number has changed.
 Completion of MATHUA 132 Math for Economics II with a grade of C or higher

MATHUA 140 Linear Algebra
4 points. Fall, Spring and Summer terms. Course homepage.
Prerequisites:
At least one (1) of the following prerequisites:
 Completion of MATHUA 009 Algebra, Trigonometry and Functions with a grade of C or higher
 SAT score of 670 or higher on mathematics portion
 ACT/ACTE Math score of 30 or higher
 Valid AP Score:
 AP Precalculus score of 4 or higher
 AP Calculus AB score of 3 or higher
 AP Calculus BC score of 3 or higher
 A Level Maths score of C or higher
 Students who took A Level Further Maths should contact the Math Department
 AS Level Maths score of B or higher
 IB Mathematics exam result from 2021  2027
 IB Analysis and Approaches HL score of 5 or higher
 IB Applications and Interpretations HL score of 5 or higher
 IB Analysis and Approaches SL score of 7
 IB Mathematics exam result from 2014  2020
 IB Mathematics HL score of 5 or higher
 IB Mathematics SL score of 6 or higher
 IB Mathematical Studies SL score of 7
 Passing Calculus/MFE I placement exam
Description:
Linear algebra is an area of mathematics devoted to the study of structurepreserving operators on special sets (linear operators on vector spaces). Linear algebra is a cornerstone of any mathematics curriculum for two very important (and related) reasons:
 The theory of linear algebra is well understood and so a first step in many areas of applied mathematics is to reduce the problem into one in linear algebra.
 The spaces and operations studied in the subject are commonplace in many different areas of mathematics, science, and engineering.
Over the semester we will study many topics that form a central part of the language of modern science. The successful student will be able to:
 Formulate, solve, apply, and interpret systems of linear equations in several variables;
 Compute with and classify matrices;
 Master the fundamental concepts of abstract vector spaces;
 Decompose linear transformations and analyze their spectra (eigenvectors and eigenvalues);
 Utilize length and orthogonality in each of the above contexts;
 Apply orthogonal projection to optimization (leastsquares) problems;
 Explore other topics (as time permits).
The material we take up in this course has applications in physics, chemistry, biology, environmental science, astronomy, economics, statistics, and just about everything else. We want you to leave the course not only with computational ability, but with the ability to use these notions in their natural scientific contexts, and with an appreciation of their mathematical beauty and power.
Students cannot take both MATHUA 140 and MATHUA 148.

MATHUA 144 Introduction To Computer Simulation
Identical to CSCIUA 330.
4 points. Spring term only. Course homepage.
Prerequisites:
Students must earn grades of C or higher in the following two prerequisite courses:
 MATHUA 121 Calculus I or MATHUA 132 Math for Economics II
 PHYSUA 11 General Physics
Description:
In this course, students will learn how to do computer simulations of such phenomena as orbits (Kepler problem and Nbody problem), epidemic and endemic disease (including evolution in response to the selective pressure of a malaria), musical stringed instruments (piano, guitar, and violin), and traffic flow in a city (with lights, breakdowns, and gridlock at corners). The simulations are based on mathematical models, numerical methods, and Matlab programming techniques that will be taught in class. The use of animations (and sound where appropriate) to present the results of simulations will be emphasized.

MATHUA 148 Honors Linear Algebra
4 points. Fall and Spring terms. Course homepage.
Prerequisites:
At least one (1) of the following prerequisites:
 Completion of MATHUA 009 Algebra, Trigonometry and Functions with a grade of C or higher
 SAT score of 670 or higher on mathematics portion
 ACT/ACTE Math score of 30 or higher
 Valid AP Score:
 AP Precalculus score of 4 or higher
 AP Calculus AB score of 3 or higher
 AP Calculus BC score of 3 or higher
 A Level Maths score of C or higher
 Students who took A Level Further Maths should contact the Math Department
 AS Level Maths score of B or higher
 IB Mathematics exam result from 2021  2027
 IB Analysis and Approaches HL score of 5 or higher
 IB Applications and Interpretations HL score of 5 or higher
 IB Analysis and Approaches SL score of 7
 IB Mathematics exam result from 2014  2020
 IB Mathematics HL score of 5 or higher
 IB Mathematics SL score of 6 or higher
 IB Mathematical Studies SL score of 7
 Passing Calculus/MFE I placement exam
Description:
This honors section of Linear Algebra is intended for wellprepared students who have already developed some mathematical maturity. Its scope will include the usual Linear Algebra (MATHUA 140) syllabus; however this class will move faster, covering additional topics and going deeper. Vector spaces, linear dependence, basis and dimension, matrices, determinants, solving linear equations, eigenvalues and eigenvectors, quadratic forms, applications such as optimization or linear regression.Students cannot take both MATHUA 140 and MATHUA 148. 
MATHUA 228 Earthâ€™s Atmosphere and Ocean: Fluid Dynamics and Climate
Identical to ENVSTUA 360.
4 points. Spring term only. Course homepage.
Prerequisites:
A grade of B+ or higher in MATHUA 122 Calculus II or MATHUA 132 Math for Economics II.
Notes: Completion of MATHUA 123 Calculus III or MATHUA 133 Math for Economics III is preferred. Students should also have some familiarity with introductory physics (even at the advanced high school level).
Description:
An introduction to the dynamical processes that drive the circulation of the atmosphere and ocean, and their interaction. This is the core of climate science. Lectures will be guided by consideration of observations and experiments, but the goal is to develop an understanding of the unifying principles of planetary fluid dynamics. Topics include the global energy balance, convection and radiation (the greenhouse effect), effects of planetary rotation (the Coriolis force), structure of the atmospheric circulation (the Hadley cell and wind patterns), structure of the oceanic circulation (winddriven currents and the thermohaline circulation), climate and climate variability (including El Nino and anthropogenic warming).

MATHUA 230 Introduction To Fluid Dynamics
Identical to PHYSUA 180.
4 points. Spring term only. Course homepage.
Prerequisites:
Students must earn grades of C or higher in the following two prerequisite courses:
 MATHUA 123 Calculus III or MATHUA 133 Math for Economics III
 PHYSUA 106 Mathematical Physics
Description:
Fluid dynamics is the branch of physics that describes motions of fluids as varied as the flow of blood in the human body, the flight of an insect or the motions of weather systems on Earth. The course introduces the key concepts of fluid dynamics: the formalism of continuum mechanics, the conservation of mass, energy and momentum in a fluid, the Euler and NavierStokes equations, viscosity and vorticity. These concepts are applied to study classic problems in fluid dynamics, such as potential flow around a cylinder, the Stokes flow, the propagation of sound and gravity waves and the onset of instability in shear flow.

MATHUA 232 Set Theory
Identical to PHILUA 73.
4 points. Offered at the discretion of the Department of Philosophy. Course homepage.
Prerequisites:
Students must have a declared major at the Math Department to be able to register for MATHUA 232.
Nonmath majors will not be able to register for MATHUA 232 and should register for PHILUA 73 instead.
Description:
Among the topics to be covered are: the axioms of set theory; Boolean operations on sets; settheoretic representation of relations, functions and orderings; the natural numbers; theory of transfinite cardinal and ordinal numbers; the axiom of choice and its equivalents; and the foundations of analysis. If time permits we may also consider some more advanced topics, such as large cardinals or the independence results.

MATHUA 233 Theory Of Probability
4 points. Fall and Spring terms. Course homepage.
Prerequisites:
Students must earn grades of C or higher in the following two prerequisite courses:
 MATHUA 123 Calculus III or MATHUA 129 Honors Calculus III or MATHUA 133 Math for Economics III
 MATHUA 140 Linear Algebra or MATHUA 148 Honors Linear Algebra
Note: This course is intended for math majors and other students with a strong interest in mathematics. It requires fluency in topics such as multivariable integration and therefore a grade of B or higher in MATHUA 123 or MATHUA 133 is strongly recommended.
Antirequisites:
 MATHUA 235 Probability & Statistics
 MATHUA 238 Honors Theory of Probability
Description:
An introduction to the mathematical treatment of random phenomena occurring in the natural, physical, and social sciences. Axioms of mathematical probability, combinatorial analysis, binomial distribution, Poisson and normal approximation, random variables and probability distributions, generating functions, Markov chains applications.
Students cannot take MATHUA 233 if they have taken MATHUA 235 or 238.

MATHUA 234 Mathematical Statistics
4 points. Fall and Spring terms. Course homepage.
Prerequisites:
MATHUA 233 Theory of Probability or MATHUA 238 Honors Theory of Probability with a grade of C or higher.
Antirequisites: MATHUA 235 Probability & Statistics
Description:
An introduction to the mathematical foundations and techniques of modern statistical analysis for the interpretation of data in the quantitative sciences. Mathematical theory of sampling; normal populations and distributions; chisquare, t, and F distributions; hypothesis testing; estimation; confidence intervals; sequential analysis; correlation, regression; analysis of variance. Applications to the sciences.
Students cannot take MATHUA 234 if they have taken MATHUA 235.

MATHUA 235 Probability And Statistics
4 points. Fall and Spring terms. Course homepage.
Prerequisites:
A grade of C or higher in MATHUA 122 Calculus II or MATHUA 132 Math for Economics II.
Antirequisites:
 MATHUA 233 Theory of Probability
 MATHUA 234 Mathematical Statistics
 MATHUA 238 Honors Theory of Probability
Description:
A combination of MATHUA 233 Theory of Probability and MATHUA 234 Mathematical Statistics at a more elementary level, so as to afford the student some acquaintance with both probability and statistics in a single term. In probability: mathematical treatment of chance; combinatorics; binomial, Poisson, and Gaussian distributions; law of large numbers and the normal approximation; application to cointossing, radioactive decay, etc. In statistics: sampling; normal and other useful distributions; testing of hypotheses; confidence intervals; correlation and regression; applications to scientific, industrial, and financial data.
Students cannot take MATHUA 235 if they have taken MATHUA 233, 234 or 238.

MATHUA 238 Honors Theory Of Probability
4 points. Spring term only. Course homepage.
Prerequisites:
Students must earn grades of B+ or higher in the following three prerequisite courses:
 MATHUA 120 Discrete Mathematics
 MATHUA 123 Calculus III or MATHUA 129 Honors Calculus III or MATHUA 133 Math for Economics III
 MATHUA 140 Linear Algebra or MATHUA 148 Honors Linear Algebra
Note: While B+ or higher is the standard requirement for this course, the department will consider petitions if you are on the borderline of that requirement.
Antirequisites:
 MATHUA 233 Theory of Probability
 MATHUA 235 Probability & Statistics
Description:
The aim of this class is to introduce students to probability theory, with a greater emphasis on rigor, more material, and a faster pace than the Theory of Probability class. The material will include discrete and continuous probability, and the most fundamental limit theorems (law of large numbers and Central Limit Theorem). Students will be made familiar with the classical models, computations on densities, and convergence to universal distributions. They will also be expected to understand the proofs of all the results seen in class, and be able to argue with mathematical rigor.
Students cannot take MATHUA 238 if they have taken MATHUA 233 or 235.

MATHUA 240 Combinatorics
4 points. Spring term only. Course homepage.
Prerequisites:
A grade of C or higher in MATHUA 122 Calculus II or MATHUA 132 Math for Economics II.
Description:
Techniques for counting and enumeration including generating functions, the principle of inclusion and exclusion, and Polya counting. Graph theory. Modern algorithms and data structures for graphtheoretic problems.

MATHUA 248 Theory Of Numbers
4 points. Fall term only. Course homepage.
Prerequisites:
A grade of C or higher in MATHUA 122 Calculus II or MATHUA 132 Math for Economics II.
Description:
Divisibility theory and prime numbers. Linear and quadratic congruences. The classical numbertheoretic functions. Continued fractions. Diophantine equations.

MATHUA 250 Mathematics of Finance
4 points. Fall and Spring terms. Course homepage.
Prerequisites:
Students must earn grades of C+ or higher in the following three prerequisite courses:
 MATHUA 123 Calculus III or MATHUA 129 Honors Calculus III or MATHUA 133 Math for Economics III
 MATHUA 140 Linear Algebra or MATHUA 148 Honors Linear Algebra
 An introductory course in probability or statistics. Acceptable courses include:
 MATHUA 233 Theory of Probability
 MATHUA 234 Mathematical Statistics
 MATHUA 235 Probability & Statistics
 MATHUA 238 Honors Theory of Probability
 ECONUA 18 Statistics
 ECONUA 20 Analytical Statistics
 STATUB 103 Statistics for Business Control and Regression Models
Description:
Introduction to the mathematics of finance. Topics include: Linear programming with application pricing and quadratic. Interest rates and present value. Basic probability: random walks, central limit theorem, Brownian motion, lognormal model of stock prices. BlackScholes theory of options. Dynamic programming with application to portfolio optimization.

MATHUA 251 Introduction to Mathematical Modeling
4 points. Fall and Spring terms. Course homepage.
Prerequisites:
Students must earn grades of C or higher in the following two prerequisite courses:
 MATHUA 123 Calculus III or MATHUA 129 Honors Calculus III or MATHUA 133 Math for Economics III
 MATHUA 140 Linear Algebra or MATHUA 148 Honors Linear Algebra
Description:
Formulation and analysis of mathematical models. Mathematical tool include dimensional analysis, optimization, simulation, probability, and elementary differential equations. Applications to biology, sports, economics, and other areas of science. The necessary mathematical and scientific background will be developed as needed. Students will participate in formulating models as well as in analyzing them.

MATHUA 252 Numerical Analysis
4 points. Fall and Spring terms. Course homepage.
Prerequisites:
Students must earn grades of C or higher in the following two prerequisite courses:
 MATHUA 123 Calculus III or MATHUA 129 Honors Calculus III or MATHUA 133 Math for Economics III
 MATHUA 140 Linear Algebra or MATHUA 148 Honors Linear Algebra
Antirequisite: MATHUA 258 Honors Numerical Analysis
Description:
In numerical analysis one explores how mathematical problems can be analyzed and solved with a computer. As such, numerical analysis has very broad applications in mathematics, physics, engineering, finance, and the life sciences. This course gives an introduction to this subject for mathematics majors. Theory and practical examples using Matlab will be combined to study a range of topics ranging from simple rootfinding procedures to differential equations and the finite element method.
Students cannot take both MATHUA 252 and 258.

MATHUA 253 Linear and Nonlinear Optimization
4 points. Fall and Spring terms. Course homepage.
Prerequisites:
Students must earn grades of C or higher in the following two prerequisite courses:
 MATHUA 123 Calculus III or MATHUA 129 Honors Calculus III or MATHUA 133 Math for Economics III
 MATHUA 140 Linear Algebra or MATHUA 148 Honors Linear Algebra
Description:
Optimization is a major part of the toolbox of the applied mathematician, and more broadly of researchers in quantitative sciences including economics, data science, machine learning, and quantitative social sciences. This course provides an applicationoriented introduction to linear programming and convex optimization, with a balanced combination of theory, algorithms, and numerical implementation. While no prior experience in programming is expected, the required coursework will include numerical implementations, including some programming; students will be introduced to appropriate computational tools, with which they will gain experience as they do the numerical assignments. Theoretical topics will include linear programming, convexity, duality, minimax theorems, and dynamic programming. Algorithmic topics will include the simplex method for linear programming, selected techniques for smooth multidimensional optimization (eg Newton's method and the conjugate gradient method), techniques for solving for L1type optimizations, and stochastic gradient descent. Applications will be drawn from many areas, but will emphasize economics (eg twoperson zerosum games, matching and assignment problems, optimal resource allocation), data science (eg regression, convexrelaxationbased approaches to sparse inverse problems, tuning of neural networks, prediction with expert advice) and operations research (eg shortest paths in networks and optimization of network flows). 
MATHUA 255 Mathematics In Medicine And Biology
Identical to BIOLUA 255.
4 points. Fall term only. Course homepage.
Prerequisites:
Students must earn grades of C or higher in the following two prerequisite courses:
 MATHUA 121 Calculus I or MATHUA 132 Math for Economics II
 BIOLUA 11 Principles of Biology I or permission from the instructor
Description:
Intended primarily for premedical students with interest and ability in mathematics. Topics of medical importance using mathematics as a tool: control of the heart, optimal principles in the lung, cell membranes, electrophysiology, countercurrent exchange in the kidney, acidbase balance, muscle, cardiac catheterization, computer diagnosis. Material from the physical sciences and mathematics is introduced as needed and developed within the course.

MATHUA 256 Computers In Medicine And Biology
Identical to BIOLUA 256.
4 points. Spring term only. Course homepage.
Prerequisites:
A grade of C or higher in MATHUA 255 Mathematics in Medicine and Biology, or permission from the instructor.
Note: Familiarity with a programming language is recommended, but not required. The course uses MATLAB, but prior experience with MATLAB is not required.
Description:
Introduces students to the use of computer simulation as a tool for investigating biological phenomena. The course requirement is to construct three computer models during the semester, to report on results to the class, and to hand in a writeup describing each project. These projects can be done individually, or as part of a team. Topics discussed in class are the circulation of the blood, gas exchange in the lung, electrophysiology of neurons and neural networks, the renal countercurrent mechanism, crossbridge dynamics in muscle, and the dynamics of epidemic and endemic diseases. Projects are normally chosen from this list, but may be chosen otherwise by students with other interests.

MATHUA 258 Honors Numerical Analysis
4 credits. Spring term only. Course homepage.
Prerequisites:
Students must earn grades of A or higher in the following two prerequisite courses:
 MATHUA 123 Calculus III or MATHUA 133 Math for Economics III
 Alternative: MATHUA 129 Honors Calculus III with a grade of B+ or higher
 MATHUA 140 Linear Algebra
 Alternative: MATHUA 148 Honors Linear Algebra with a grade of B+ or higher
Notes: Programming experience is strongly recommended (e.g. Julia, Matlab, or NumPy), but not required (there is a programming component to this course).
Antirequisite: MATHUA 252 Numerical Analysis
Description:
Covers the analysis of numerical algorithms which are ubiquitously used to solve problems throughout mathematics, physics, engineering, finance, and the life sciences. Topics include: algorithms for solving nonlinear equations; optimization; finding eigenvalues/eigenvectors of matrices; computing matrix factorizations and performing linear regressions; function interpolation, approximation, and integration; basic signal processing using the Fast Fourier Transform; Monte Carlo simulation. An introduction to programming will be provided as it is an integral part of numerical analysis, but students should feel quite comfortable programming on their own (or be exceptionally willing to learn along the way).
Students cannot take both MATHUA 252 and 258.
 MATHUA 123 Calculus III or MATHUA 133 Math for Economics III

MATHUA 262 Ordinary Differential Equations
4 credits. Fall and Spring terms. Course homepage.
Prerequisites:
Students must earn grades of C or higher in the following two prerequisite courses:
 MATHUA 123 Calculus III or MATHUA 129 Honors Calculus III or MATHUA 133 Math for Economics III
 MATHUA 140 Linear Algebra or MATHUA 148 Honors Linear Algebra
Antirequisite: MATHUA 268 Honors Ordinary Differential Equations
Description:
A first course in ordinary differential equations, including analytical solution methods, elementary numerical methods, and modeling. Topics to be covered include: firstorder equations including integrating factors; secondorder equations including variation of parameters; series solutions; elementary numerical methods including Euler's methods, RungeKutta methods, and error analysis; Laplace transforms; systems of linear equations; boundaryvalue problems. Some optional topics to be chosen at the instructor's discretion include: nonlinear dynamics including phaseplane description; elementary partial differential equations and Fourier series.
Students cannot take both MATHUA 262 and 268.

MATHUA 263 Partial Differential Equations
4 credits. Fall and Spring terms. Course homepage.
Prerequisites:
A grade of C or higher in MATHUA 262 Ordinary Differential Equations or MATHUA 268 Honors Ordinary Differential Equations.
Description:
Many laws of physics are formulated as partial differential equations. This course discusses the simplest examples, such as waves, diffusion, gravity, and static electricity. Nonlinear conservation laws and the theory of shock waves are discussed. Further applications to physics, chemistry, biology, and population dynamics.

MATHUA 264 Chaos And Dynamical Systems
4 credits. Spring term only. Course homepage.
Prerequisites:
Students must earn grades of C or higher in the following two prerequisite courses:
 MATHUA 122 Calculus II or MATHUA 132 Math for Economics II
 MATHUA 140 Linear Algebra or MATHUA 148 Honors Linear Algebra
Description:
Topics will include dynamics of maps and of first order and secondorder differential equations: stability, bifurcations, limit cycles, dissection of systems with fast and slow time scales. Geometric viewpoint, including phase planes, will be stressed. Chaotic behavior will be introduced in the context of onevariable maps (the logistic), fractal sets, etc. Applications will be drawn from physics and biology. There will be homework and projects, and a few computer lab sessions (programming experience is not a prerequisite).

MATHUA 268 Honors Ordinary Differential Equations
4 credits. Fall term only. Course homepage.
Prerequisites:
 A grade of B+ or higher in MATHUA 328 Honors Analysis I
 Alternative: a grade of A or higher in MATHUA 325 Analysis
Description:
This class will develop rigorously the basic theory of Ordinary Differential Equations (ODEs). Existence and uniqueness of solutions to ODEs are first investigated, for linear and nonlinear problems, set on the real line or the complex plane. More qualitative questions are then considered, about the behavior of the solutions, with possible prolongations to various topics in Dynamical Systems theory. Applications to Physics and Biology will appear naturally when discussing examples.
 A grade of B+ or higher in MATHUA 328 Honors Analysis I

MATHUA 282 Functions of a Complex Variable
4 credits. Spring term only. Course homepage.
Prerequisites:
Students must earn grades of C or higher in the following two prerequisite courses:
 MATHUA 123 Calculus III or MATHUA 129 Honors Calculus III or MATHUA 133 Math for Economics III
 MATHUA 140 Linear Algebra or MATHUA 148 Honors Linear Algebra
Description:
Complex numbers and complex functions. Differentiation and the CauchyRiemann equations. Cauchy's theorem and the Cauchy integral formula. Singularities, residues, and Laurent series. Fractional Linear transformations and conformal mapping. Analytic continuation. Applications to fluid flow etc.

MATHUA 325 Analysis
4 credits. Fall and Spring terms. Course homepage.
Prerequisites:
Students must earn grades of C or higher in the following two prerequisite courses:
 MATHUA 123 Calculus III or MATHUA 129 Honors Calculus III or MATHUA 133 Math for Economics III
 MATHUA 140 Linear Algebra or MATHUA 148 Honors Linear Algebra
Antirequisite: MATHUA 328 Honors Analysis I
Description:
This course is an introduction to rigorous analysis on the real line. Topics include: the real number system, sequences and series of numbers, functions of a real variable (continuity and differentiability), the Riemann integral, basic topological notions in a metric space, sequences and series of functions including Taylor and Fourier series.
Students cannot take both MATHUA 325 and MATHUA 328.

MATHUA 328 Honors Analysis I
4 credits. Fall term only. Course homepage.
Prerequisites:
Students must earn grades of A or higher in the following two prerequisite courses:
 MATHUA 123 Calculus III or MATHUA 133 Math for Economics III
 Alternative: MATHUA 129 Honors Calculus III with a grade of B+ or higher
 MATHUA 140 Linear Algebra
 Alternative: MATHUA 148 Honors Linear Algebra with a grade of B+ or higher
Antirequisite: MATHUA 325 Analysis
Description:
This is an introduction to the rigorous treatment of the foundations of real analysis in one variable. It is based entirely on proofs. Students are expected to know what a mathematical proof is and are also expected to be able to read a proof before taking this class. Topics include: properties of the real number system, sequences, continuous functions, topology of the real line, compactness, derivatives, the Riemann integral, sequences of functions, uniform convergence, infinite series and Fourier series. Additional topics may include: Lebesgue measure and integral on the real line, metric spaces, and analysis on metric spaces.
Students cannot take both MATHUA 325 and MATHUA 328.
 MATHUA 123 Calculus III or MATHUA 133 Math for Economics III

MATHUA 329 Honors Analysis II
4 credits. Spring term only. Course homepage.
Prerequisites:
 A grade of C or higher in MATHUA 328 Honors Analysis I
 Alternative: a grade of A in MATHUA 325 Analysis and receive permission from the Honors Algebra II instructor
Description:
This is a continuation of MATHUA 328 Honors Analysis I. Topics include: metric spaces, differentiation of functions of several real variables, the implicit and inverse function theorems, Riemann integral on Rn, Lebesgue measure on Rn, the Lebesgue integral.
 A grade of C or higher in MATHUA 328 Honors Analysis I

MATHUA 343 Algebra
4 credits. Fall and Spring terms. Course homepage.
Prerequisites:
Students must earn grades of C or higher in the following two prerequisite courses:
 MATHUA 123 Calculus III or MATHUA 129 Honors Calculus III or MATHUA 133 Math for Economics III
 MATHUA 140 Linear Algebra or MATHUA 148 Honors Linear Algebra
Note: It is strongly recommended, but not required, that students complete MATHUA 325 Analysis before registering for MATHUA 343 Algebra.
Antirequisite: MATHUA 348 Honors Algebra I
Description:
Introduction to abstract algebraic structures, including groups, rings, and fields. Sets and relations. Congruences and unique factorization of integers. Groups, permutation groups, homomorphisms and quotient groups. Rings and quotient rings, Euclidean rings, polynomial rings. Fields, finite extensions.
Students cannot take both MATHUA 343 and MATHUA 348.

MATHUA 348 Honors Algebra I
4 credits. Fall term only. Course homepage.
Prerequisites:
Students must earn grades of A or higher in the following two prerequisite courses:
 MATHUA 123 Calculus III or MATHUA 133 Math for Economics III
 Alternative: MATHUA 129 Honors Calculus III with a grade of B+ or higher
 MATHUA 140 Linear Algebra
 Alternative: MATHUA 148 Honors Linear Algebra with a grade of B+ or higher
Notes: It is strongly recommended, but not required, that students complete MATHUA 325 Analysis or MATHUA 328 Honors Analysis I before registering for MATHUA 348 Honors Algebra I.
Antirequisite: MATHUA 343 Algebra
Description:
Introduction to abstract algebraic structures, including groups, rings, and fields. Sets and relations. Congruences and unique factorization of integers. Groups, permutation groups, group actions, homomorphisms and quotient groups, direct products, classification of finitely generated abelian groups, Sylow theorems. Rings, ideals and quotient rings, Euclidean rings, polynomial rings, unique factorization.
Students cannot take both MATHUA 343 and MATHUA 348.
 MATHUA 123 Calculus III or MATHUA 133 Math for Economics III

MATHUA 349 Honors Algebra II
4 credits. Spring term only. Course homepage.
Prerequisites:
 A grade of C or higher in MATHUA 348 Honors Algebra I
 Alternative: a grade of A in MATHUA 343 Algebra and receive permission from the Honors Algebra II instructor
Description:
Principle ideal domains, polynomial rings in several variables, unique factorization domains. Fields, finite extensions, constructions with ruler and compass, Galois theory, solvability by radicals.
 A grade of C or higher in MATHUA 348 Honors Algebra I

MATHUA 375 Topology
4 credits. Spring term only. Course homepage.
Prerequisites:
A grade of C or higher in MATHUA 325 Analysis or MATHUA 328 Honors Analysis I.
Description:
Settheoretic preliminaries. Metric spaces, topological spaces, compactness, connectedness, covering spaces, and homotopy groups.

MATHUA 377 Differential Geometry
4 credits. Spring term only. Course homepage.
Prerequisites:
Students must earn grades of C or higher in the following two prerequisite courses:
 MATHUA 123 Calculus III or MATHUA 129 Honors Calculus III or MATHUA 133 Math for Economics III
 MATHUA 140 Linear Algebra or MATHUA 148 Honors Linear Algebra
Note: It is strongly recommended, but not required, that students have completed MATHUA 325 Analysis or MATHUA 328 Honors Analysis I before registering for MATHUA 377 Differential Geometry.
Description:
The geometry of curves and surfaces in Euclidean space. Frenet formulas, the isoperimetric inequality, local theory of surfaces in Euclidean space, first and second fundamental forms. Gaussian and mean curvature, isometries, geodesics, parallelism, the GaussBonnet Theorem.

MATHUA 393 Honors I
4 credits. Offered in the fall of even years. Course homepage.
Prerequisites:
Honors standing or approval of the director of the honors program.
Prerequisite varies according to topic.
Description:
A lecture/seminar course on advanced topics. Topics vary yearly and are updated from time to time. Detailed course descriptions are available during preregistration.

MATHUA 394 Honors II
4 credits. Offered in the spring of odd years. Course homepage.
Prerequisites:
Honors standing or approval of the director of the honors program.
Prerequisite varies according to topic.
Description:
A lecture/seminar course on advanced topics. Topics vary yearly and are updated from time to time. Detailed course descriptions are available during preregistration.

MATHUA 395 Special Topics I
4 credits. Offered on request in the Fall. Course homepage.
Prerequisites:
Prerequisite varies according to topic.
Description:
Please see Albert for course topic and description.

MATHUA 396 Special Topics II
4 credits. Offered on request in the Fall. Course homepage.
Prerequisites:
Prerequisite varies according to topic.
Description:
Please see Albert for course topic and description.

MATHUA 397 Honors III
4 credits. Offered in the fall of odd years. Course homepage.
Prerequisites:
Honors standing or approval of the director of the honors program.
Prerequisite varies according to topic.
Description:
A lecture/seminar course on advanced topics. Topics vary yearly and are updated from time to time. Detailed course descriptions are available during preregistration.

MATHUA 398 Honors IV
4 credits. Offered in the spring of even years. Course homepage.
Prerequisites:
Honors standing or approval of the director of the honors program.
Prerequisite varies according to topic.
Description:
A lecture/seminar course on advanced topics. Topics vary yearly and are updated from time to time. Detailed course descriptions are available during preregistration.

MATHUA 897 Internship
2 or 4 credits. Offered in the Fall and first Summer Session. Course homepage.
Prerequisites:
Permission of the department. Student must be a declared Math major, have a math GPA of 3.5 and an overall GPA of 3.0, and have at least 50% of the Math major courses completed.
Description:
To register for this course a student must complete the Enrollment Request Form and have the approval of the Director of Undergraduate Studies.

MATHUA 898 Internship
2 or 4 credits. Offered in the Spring and second Summer Session. Course homepage.
Prerequisites:
Permission of the department. Student must be a declared Math major, have a math GPA of 3.5 and an overall GPA of 3.0, and have at least 50% of the Math major courses completed.
Description:
To register for this course a student must complete the Enrollment Request Form and have the approval of the Director of Undergraduate Studies.

MATHUA 997 Independent Study
2 or 4 credits. Offered in the Fall and first Summer Session. Course homepage.
Prerequisites:
Permission of the department.
Description:
To register for this course a student must complete an application form for Independent Study and have the approval of a faculty sponsor and the Director of Undergraduate Studies.

MATHUA 998 Independent Study
2 or 4 credits. Offered in the Spring and second Summer Session. Course homepage.
Prerequisites:
Permission of the department.
Description:
To register for this course a student must complete an application form for Independent Study and have the approval of a faculty sponsor and the Director of Undergraduate Studies.