Courses

MATH B100 Introduction to Calculus

Not offered 2022-23

This course introduces the concepts and skills that provide a foundation for calculus, the study of how things change. Functions that provide useful models for studying the change of a wide variety of phenomena will be introduced and analyzed through the concepts of limits and derivatives.

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MATH B101 Calculus I

Fall 2022, Spring 2023

This is the first in a sequence of two courses that covers single-variable calculus. Topics include functions, limits, continuity, derivatives, differentiation formulas, applications of derivatives, integrals, and the fundamental theorem of calculus. Prerequisite: proficiency in high-school mathematics (including algebra, geometry, and trigonometry).

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MATH B101L Calculus I lab

Fall 2022, Spring 2023

This lab course will reinforce the concepts and skills that are needed to be successful in Calculus 1. Students must be enrolled in MATH B101 Calculus I to enroll in this course.

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MATH B102 Calculus II

Fall 2022, Spring 2023

This is the second in a sequence of two courses that covers single-variable calculus. Topics include techniques of integration, applications of integration, infinite sequences and series, tests of convergence for series, and power series. Prerequisite: a merit grade in Math 101 (or an equivalent experience).

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MATH B104 Basic Probability and Statistics

Fall 2022, Spring 2023

This course introduces key concepts in descriptive and inferential statistics. Topics include summary statistics, graphical displays, correlation, regression, probability, the Law of Large Numbers, expected value, standard error, the Central Limit Theorem, hypothesis testing, sampling procedures, bias, and the use of statistical software.

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MATH B195 Select Topics in Mathematics

Section 001 (Fall 2022): Intro to Math & Sustainability

Fall 2022

This is a topics course. Course content varies.

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MATH B201 Multivariable Calculus

Fall 2022

This course extends calculus to functions of multiple variables. Topics include functions, limits, continuity, vectors, directional derivatives, optimization problems, multiple integrals, parametric curves, vector fields, line integrals, surface integrals, and the theorems of Gauss, Green and Stokes. Prerequisite: a merit grade in Math 102 (or an equivalent experience).

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MATH B203 Linear Algebra

Spring 2023

This course considers systems of linear equations, matrix algebra, determinants, vector spaces, subspaces, linear independence, bases, dimension, linear transformations, eigenvalues, eigenvectors, orthogonality, and applications of linear algebra. Prerequisite (or corequisite): Math 102.

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MATH B205 Theory of Probability with Applications

Not offered 2022-23

The course analyzes repeatable experiments in which short-term outcomes are uncertain, but long-run behavior is predictable. Topics include: random variables, discrete distributions, continuous densities, conditional probability, expected value, variance, the Law of Large Numbers, and the Central Limit Theorem. Prerequisite: Math 201.

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MATH B206 Transition to Higher Mathematics

Spring 2023

This course focuses on mathematical writing and proof techniques. Topics include symbolic logic, set notation and quantifiers, proof by contradiction and induction, set notation and operations, relations and partitions, functions, and more. Prerequisite (or corequisite): Math 203.

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MATH B208 Introduction to Modeling and Simulation

Fall 2022

Mathematical models are constructed to describe the complex world within and around us. Computational methods are employed to visualize and solve these models. In this course, we focus on developing mathematical models to describe real-world phenomena, while using computer simulations to examine prescribed and/or random behavior of various systems. The course includes an introduction to programming (in R or Matlab/Octave), and mathematical topics may include discrete dynamical systems, model fitting using least squares, elementary stochastic processes, and linear models (regression, optimization, linear programming). Applications to economics, biology, chemistry, and physics will be explored. Prior programming experience not required.

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MATH B210 Differential Equations with Applications

Fall 2022

Ordinary differential equations, including general first-order equations, linear equations of higher order and systems of equations, via numerical, geometrical, and analytic methods. Applications to physics, biology, and economics. Co-requisite: MATH 201 or 203.

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MATH B221 Introduction to Topology and Geometry

Not offered 2022-23

An introduction to the ideas of topology and geometry through the study of knots and surfaces in three-dimensional space. The course content may vary from year to year, but will generally include some historical perspectives and some discussion of connections with the natural and life sciences. Co-requisite: MATH 201 or 203.

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MATH B225 Introduction to Financial Mathematics

Spring 2023

Topics to be covered include market conventions and instruments, Black-Scholes option-pricing model, and practical aspects of trading and hedging. All necessary definitions from probability theory (random variables, normal and lognormal distribution, etc.) will be explained. Prerequisite: MATH 102. ECON 105 is recommended.

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MATH B290 Elementary Number Theory

Spring 2023

Properties of the integers, divisibility, primality and factorization, congruences, Chinese remainder theorem, multiplicative functions, quadratic residues and quadratic reciprocity, continued fractions, and applications to computer science and cryptography. Prerequisite: MATH 102.

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MATH B295 Select Topics in Mathematics

Section 001 (Fall 2022): History of Math
Section 001 (Fall 2023): Math Modeling and Sustainability
Section 001 (Spring 2024): Statistics with R

Fall 2022

This is a topics course. Course content varies. Not all topics are open to first year students.

Current topic description: In this course, we will use mathematics to study issues of sustainability. How much energy does a typical person in the United States use? What is the carbon footprint associated with this energy use? Is it possible to meet all of our energy needs using renewable energy? How can we carry out a cost-benefit analysis to determine if a particular energy-saving device is "worth it"? The course has a Praxis component: students will work in teams to analyze a real world sustainability issue of interest to a community partner.

Current topic description: This course introduces descriptive and inferential statistics through work with real data and programming in R (statistical computing and graphics software). Topics include: introduction to data, data visualization, sample statistics, probability, sampling variability, confidence intervals, hypothesis testing, inference for categorical and numerical data, outliers, statistical models, and confounding.

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MATH B301 Real Analysis I

Fall 2022

A first course in real analysis, providing a rigorous development of single variable calculus, with a strong focus on proof writing. Topics covered: the real number system, elements of set theory and topology, limits, continuous functions, the intermediate and extreme value theorems, differentiable functions and the mean value theorem, uniform continuity, the Riemann integral, the fundamental theorem of calculus. Possible additional topics include analysis on metric spaces or dynamical systems. Prerequisite: MATH 201. Some students also find it helpful to have taken a transitional course such as MATH 206 before enrolling in this course.

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MATH B302 Real Analysis II

Spring 2023

A continuation of Real Analysis I: Infinite series, power series, sequences and series of functions, pointwise and uniform convergence, and additional topics selected from: Fourier series, calculus of variations, the Lebesgue integral, dynamical systems, and calculus in higher dimensions. Prerequisite: MATH 301.

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MATH B303 Abstract Algebra I

Fall 2022

A first course in abstract algebra, including an introduction to groups, rings and fields, and their homomorphisms. Topics covered: cyclic and dihedral groups, the symmetric and alternating groups, direct products and finitely generated abelian groups, cosets, Lagrange's Theorem, normal subgroups and quotient groups, isomorphism theorems, integral domains, polynomial rings, ideals, quotient rings, prime and maximal ideals. Possible additional topics include group actions and the Sylow Theorems, free abelian groups, free groups, PIDs and UFDs. Prerequisite: MATH 203. Some students also find it helpful to have taken a transitional course such as MATH 206 before enrolling in this course.

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MATH B304 Abstract Algebra II

Spring 2023

A continuation of Abstract Algebra I. Vector spaces and linear algebra, field extensions, algebraic and transcendental extensions, finite fields, fields of fractions, field automorphisms, the isomorphism extension theorem, splitting fields, separable and inseparable extensions, algebraic closures, and Galois theory. Also, if not covered in Abstract Algebra I: group actions and Sylow theorems, free abelian groups, free groups, PIDs and UFDs. Possible additional topic: finitely generated modules over a PID and canonical forms of matrices. Prerequisite: MATH 303.

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MATH B308 Applied Mathematics I

Spring 2023

This course will provide a general introduction to methods and modeling in applied mathematics. A variety of mathematical tools will be used to develop and study a wide range of models, including deterministic, discrete, and stochastic methods. Additional emphasis will be placed on techniques for analyzing mathematical models, including phase plane methods, stability analysis, dimensional analysis, bifurcation theory, and computer simulations. Applications to biology, physics, chemistry, engineering, and the social sciences may be discussed. Prerequisite: Math 203 or equivalent, or permission from instructor

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MATH B310 Introduction to the Mathematics of Financial Derivatives

Not offered 2022-23

An introduction to the mathematics utilized in the pricing models of derivative instruments. Topics to be covered may include Arbitrage Theorem, pricing derivatives, Wiener and Poisson processes, martingales and martingale representations, Ito's Lemma, Black-Scholes partial differentiation equation, Girsanov Theorem and Feynman-Kac Formula. Prerequisite: MATH 201 or permission of instructor.

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MATH B312 Topology

Fall 2022

General topology (topological spaces, continuity, compactness, connectedness, quotient spaces), the fundamental group and covering spaces, introduction to geometric topology (classification of surfaces, manifolds). Typically offered yearly in alternation with Haverford. Co-requisite: MATH 301, MATH 303, or permission of instructor.

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MATH B322 Functions of Complex Variables

Not offered 2022-23

Analytic functions, Cauchy's theorem, Laurent series, calculus of residues, conformal mappings, Moebius transformations. Prerequisite: MATH 301 or permission of instructor.

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MATH B325 Advanced Topics in Applied Mathematics

Not offered 2022-23

This topics course will focus on one advanced area in applied mathematics. Topics may include numerical linear algebra, applied partial differential equations, optimal control, parameter estimation and model fitting.

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MATH B390 Number Theory

Not offered 2022-23

Study of integers with an emphasis on their multiplicative structure and topics related to analysis, and a first course in analytic number theory. Core topics: divisibility and primes, arithmetic functions, average and extremal orders, techniques of analytic number theory, Riemann zeta function, prime number theorem, Dirichlet characters, L-functions. Possible additional topics may include approximations by rational numbers, geometry of numbers, algebraic numbers and class numbers, sums of squares, and the idea of modular forms.Prerequisite: Math 201, and some familiarity with writing proofs (such as Math 206, Math 301/303 as a co-requisite, or permission of instructor)

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MATH B398 Senior Conference

A seminar for seniors majoring in mathematics. Topics vary from year to year.

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MATH B399 Senior Conference

A seminar for seniors majoring in mathematics. Topics vary from year to year.

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MATH B400 Senior Thesis

Independent research for senior thesis in Math

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MATH B403 Supervised Work

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MATH B501 Graduate Real Analysis I

Fall 2022

In this course we will study the theory of measure and integration. Topics will include Lebesgue measure, measurable functions, the Lebesgue integral, the Riemann-Stieltjes integral, complex measures, differentiation of measures, product measures, and L^p spaces.

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MATH B502 Graduate Real Analysis II

Spring 2023

This course is a continuation of Math 501.

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MATH B503 Graduate Algebra I

Not offered 2022-23

This is the first course in a two course sequence providing a standard introduction to algebra at the graduate level. Topics in the first semester will include categories, groups, rings, modules, and linear algebra.

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MATH B504 Graduate Algebra II

Not offered 2022-23

This course is a continuation of Math 503, the two courses providing a standard introduction to algebra at the graduate level. Topics in the second semester will include linear algebra, fields, Galois theory, and advanced group theory. Prerequisite: MATH B503.

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MATH B512 General Topology

Fall 2022

This course covers the basic notions of point set topology, with an introduction to algebraic and geometric topology. Topics covered include topological spaces, continuity, compactness, connectedness, quotient spaces, the fundamental group and covering spaces, and the classification of surfaces.

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MATH B522 Complex Analysis

Not offered 2022-23

This course covers the basic notions of complex analysis. Topics covered include analytic functions, Cauchy's theorem, the calculus of residues, conformal mappings, Riemann mapping theorem and Picard's little theorem.

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MATH B525 Algebraic Topology

Spring 2023

This course covers the basic notions of algebraic topology. Topics covered include homology theory, cohomology theory, duality on manifolds, and an introduction to homotopy theory.

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MATH B530 Differential Topology

Not offered 2022-23

This course covers the basic notions of differential topology. Topics covered include smooth manifolds, smooth maps, differential forms, and integration on manifolds.

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MATH B701 Supervised Work

Fall 2022, Spring 2023

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MATH B701 Supervised Work

Not offered 2022-23

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MATH B702 Research Seminar

Fall 2022, Spring 2023

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MATH B702 Research Seminar

Not offered 2022-23

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CHEM B221 Physical Chemistry I

Fall 2022

Introduction to quantum theory and spectroscopy. Atomic and molecular structure; molecular modeling; rotational, vibrational, electronic and magnetic resonance spectroscopy. Lecture three hours. Prerequisites: CHEM B104 and MATH B201.

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CMSC B231 Discrete Mathematics

Fall 2022

An introduction to discrete mathematics with strong applications to computer science. Topics include propositional logic, proof techniques, recursion, set theory, counting, probability theory and graph theory. Co-requisites: BIOL B115 or CMSC B109 or CMSC B113 or CMSC H105 or CMSC H107.

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CMSC B311 Computational Geometry

Spring 2023

A study of algorithms and mathematical theories that focus on solving geometric problems in computing, which arise naturally from a variety of disciplines such as Computer Graphics, Computer Aided Geometric Design, Computer Vision, Robotics and Visualization. The materials covered sit at the intersection of pure Mathematics and application-driven Computer Science and efforts will be made to accommodate Math majors and Computer Science majors of varying math/computational backgrounds. Topics include: graph theory, triangulation, convex hulls, geometric structures such as Voronoi diagrams and Delaunay triangulations, as well as curves and polyhedra surface topology. Prerequisite: CMSC/MATH B/H231 and CMSC B151 or CMSC/MATH B/H231 and CMSC H106 or CMSC/MATH B/H231 and CMSC H107.

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CMSC B340 Analysis of Algorithms

Fall 2022

This course will cover qualitative and quantitative analysis of algorithms and their corresponding data structures from a precise mathematical point of view. Topics include: performance bounds, asymptotic and probabilistic analysis, worst case and average case behavior and correctness and complexity. Particular classes of algorithms will be studied in detail. This course fulfills the writing requirement in the major. Prerequisites: CMSC B151, or CMSC H106/107, and CMSC B231; or permission of instructor.

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ECON B304 Econometrics

Spring 2023

The econometric theory presented in ECON 253 is further developed and its most important empirical applications are considered. Each student does an empirical research project using multiple regression and other statistical techniques. Prerequisites:ECON B253 or ECON H203 or ECON H204 and ECON B200 or ECON B202 and MATH B201 or permission of instructor.

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PHYS B205 Mathematical Methods in the Sciences 1

Not offered 2022-23

This course is the first of two half-semester sessions which presents topics in applied mathematics useful to students in physics, engineering, physical chemistry, geology, and computer science. This first session will cover infinite series, complex variables, Fourier series, integral transforms, special functions, and ordinary differential equations. Lecture three hours and additional recitation sessions as needed. Prerequisite: MATH B102.

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PHYS B207 Mathematical Methods in the Sciences II

Not offered 2022-23

This course is the second of two half-semester sessions which presents topics in applied mathematics useful to students in physics, engineering, physical chemistry, geology, and computer science. This second session covers advanced ordinary differential equations, partial differential equations, special functions, series solutions, and boundary-value problems. Lecture three hours and additional recitation sessions as needed. Prerequisite: PHYS B205, MATH B201 and MATH B203

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PHYS B306 Mathematical Methods in the Physical Sciences

Fall 2022

This course presents topics in applied mathematics useful to students, including physicists, engineers, physical chemists, geologists, and computer scientists studying the natural sciences. Topics are taken from Fourier series, integral transforms, advanced ordinary and partial differential equations, special functions, boundary-value problems, functions of complex variables, and numerical methods. Lecture three hours and additional recitation sessions as needed. Prerequisite: MATH 201 and 203.

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PHYS B328 Galactic Dynamics & Advanced Classical Mechanics

Not offered 2022-23

This course is for the advanced undergraduate interested in the physics galactic dynamics and evolution, i.e. collisionless, gravitational N-body systems composed of stars and dark matter. Topics covered will include potential theory, orbit theory, collisionless Boltzmann equation, Jeans equations, disk stability, violent relaxation, phase mixing, dynamical friction and kinetic theory. To support the these theories, we will also cover advanced topics in classical mechanics including Lagrange & Hamilton methods, the central force problem, canonical transformations, action-angle variables, chaos and perturbation theory. This course is taught in a seminar format, in which students are responsible for presenting much of the course material in class meetings. Prerequisites: MATH B201, MATH B203, PHYS B201, B214, and PHYS B308 or permission from instructor.

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