Â鶹AV

MATH B101 Calculus I

Fall 2024, Spring 2025

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).

Quantitative Methods (QM)

Quantitative Readiness Required (QR)

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MATH B101L Calculus I lab

Fall 2024, Spring 2025

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 2024, Spring 2025

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).

Quantitative Methods (QM)

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MATH B104 Basic Probability and Statistics

Fall 2024, Spring 2025

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.

Quantitative Methods (QM)

Quantitative Readiness Required (QR)

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MATH B195 Select Topics in Mathematics

Not offered 2024-25

This is a topics course. Course content varies.

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MATH B201 Multivariable Calculus

Fall 2024, Spring 2025

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).

Quantitative Methods (QM)

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MATH B203 Linear Algebra

Spring 2025

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.

Quantitative Methods (QM)

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MATH B205 Theory of Probability with Applications

Not offered 2024-25

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

Fall 2024, Spring 2025

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 Co-requisite: MATH B201 or MATH B203. Not open to students who have taken a 300 level Math course

Writing Intensive

Quantitative Methods (QM)

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MATH B208 Introduction to Modeling and Simulation

Spring 2025

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. Prerequisite: MATH B102 or the equivalent (merit score on the AP Calculus BC Exam or placement).

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Quantitative Methods (QM)

Quantitative Readiness Required (QR)

Counts Toward Data Science

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MATH B210 Differential Equations with Applications

Fall 2024

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 2024-25

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

Not offered 2024-25

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

Not offered 2024-25

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 2023): Math Modeling and Sustainability
Section 001 (Spring 2024): Statistics with R
Section 001 (Fall 2024): Evolutionary Game Theory
Section 001 (Spring 2025): Evolutionary Game Theory
Section 002 (Spring 2025): Codes and Ciphers
Section 003 (Spring 2025): History of Math

Fall 2024, Spring 2025

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

Current topic description: This course introduces basic concepts in evolutionary game theory (EGT) and dynamics. Evolutionary dynamics is the mathematical study of the evolutionary processes that influence biological and social processes. In this course, we will cover fundamental topics in EGT, including evolutionarily stable strategies, replicator dynamics, and games on networks. We will introduce the mathematical techniques and modeling approaches needed to study real-world problems, with a focus on social evolution and human cooperation.

Current topic description: This course introduces basic concepts in evolutionary game theory (EGT) and dynamics. Evolutionary dynamics is the mathematical study of the evolutionary processes that influence biological and social processes. In this course, we will cover fundamental topics in EGT, including evolutionarily stable strategies, replicator dynamics, and games on networks. We will introduce the mathematical techniques and modeling approaches needed to study real-world problems, with a focus on social evolution and human cooperation.

Current topic description: This course is an introduction to classical and modern methods for encoding secret messages (cryptography) and the science of breaking codes and ciphers (cryptanalysis). It blends the history of secret writing, the art of creating codes, and the mathematics underlying the theory and practice of encryption and decryption. Topics include substitution and transposition ciphers, Vigenere and Hill ciphers, statistical methods in cryptanalysis, and applications from linear algebra and number theory to cryptananalysis, digital signatures, PGP, RSA, and other public-key ciphers. Latter topics also will require use of computer applets. Prerequisites: Math B203 (Linear Algebra) or Math B206 (Transition to Higher Mathematics).

Current topic description: This course samples mathematical landmarks from Classical times to the 19th century. Among these are Euclid's proof of the Pythagorean Theorem, Archimedes' determination of cirucular area, Newton's approximation of p, Euler's solution of the Basel problem, and Catnor's theory of the infinite. We end with a look at the mathematical heritage of Â鶹AV and the "math matriarchs" who built our department. In short, the course will have historical and biographical components, but its primary object is to examine, in full mathematical detail, landmarks from the long and glorious history of mathematics. Prerequisite: Any 200-level math course.

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MATH B301 Real Analysis I

Fall 2024

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 and MATH B206 or permission of instructor.

Writing Attentive

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MATH B302 Real Analysis II

Spring 2025

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 2024, Spring 2025

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 and MATH B206 or permission from instructor.

Writing Attentive

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MATH B304 Abstract Algebra II

Spring 2025

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 2025

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 B203 and MATH B206 and MATH B210 or permission of instructor.

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MATH B310 Mathematics of Financial Derivatives

Not offered 2024-25

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 and MATH B206 or permission of instructor.

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MATH B312 Topology

Fall 2024

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 2024-25

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 2024-25

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. Prerequisite: Math B210: Differential Equations AND one of the following: Math 206, or Math B301, or permission of instructor

Quantitative Readiness Required (QR)

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MATH B390 Number Theory

Not offered 2024-25

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 MATH B206, 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 Â鶹AV Real Analysis I

Spring 2025

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 Â鶹AV Real Analysis II

Not offered 2024-25

This course is a continuation of Math 501.

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MATH B503 Â鶹AV Algebra I

Not offered 2024-25

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 Â鶹AV Algebra II

Not offered 2024-25

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 2024

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 2024-25

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

Not offered 2024-25

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 2024-25

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 2024, Spring 2025

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MATH B701 Supervised Work

Fall 2024, Spring 2025

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MATH B702 Research Seminar

Fall 2024, Spring 2025

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MATH B702 Research Seminar

Fall 2024, Spring 2025

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CHEM B221 Physical Chemistry I

Fall 2024

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.

Quantitative Methods (QM)

Counts Toward Biochemistry Molecular Biology

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CMSC B231 Discrete Mathematics

Fall 2024, Spring 2025

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. Prerequisites: CMSC B231 or CMSC H231 or MATH B231 or MATH H231.

Quantitative Methods (QM)

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CMSC B311 Computational Geometry

Spring 2025

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 B151 or CMSC H106 or CMSC H107, and CMSC B231, or CMSC H231 or MATH B231 or MATH H231, or permission of instructor.

Quantitative Readiness Required (QR)

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CMSC B340 Analysis of Algorithms

Fall 2024, Spring 2025

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 or CMSC H107, and CMSC B231, or CMSC H231 or MATH B231 or MATH H231 or permission of instructor.

Writing Intensive

Quantitative Readiness Required (QR)

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ECON B304 Econometrics

Spring 2025

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.

Counts Toward Data Science

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PHYS B205 Mathematical Methods in the Sciences I

Fall 2024

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

Fall 2024

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

Not offered 2024-25

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 2024-25

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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