# Course and Schedule Information

The Mathematics department will occasionally allow courses taken from other Boston College departments to count as electives for the mathematics major. Such courses will be decided upon before the semester they're taken, and allowable courses will be listed on the department website. **Only listed courses will be eligible for this purpose, and only for semesters for which they have been approved**. The Assistant Chair for Undergraduate Studies should be seen to have a waiver/substitution form signed to allow the course to count as a mathematics elective.

Note that a maximum of **one** course taken at Boston College outside the Mathematics department can count as an elective for the mathematics major. This does not affect courses taken abroad, which will be handled in the usual manner.

#### Course Schedules

Please use the Course Schedule Information page available at the Student Services website for complete and up-to-date course listings, including links to course descriptions, instructor information, and indications of which courses are open, closed, or restricted.

#### Course Descriptions

We've separated our undergraduate course descriptions by category (courses may be listed in more than one place).

**MATH 1004 Finite Probability and Applications (Fall/Spring: 3)**

This course is an introduction to finite combinatorics and probability, emphasizing applications. Topics include finite sets and partitions, enumeration, probability, expectation and random variables.

**MATH 1007 Ideas in Mathematics (Fall/Spring: 3)**

This course is designed to introduce the student to the spirit, beauty and vitality of mathematics. The emphasis is on development of ideas rather than problem solving skills. Topics vary, but are typically chosen from diverse areas such as geometry, number theory, computation and graph theory.

**MATH 1180 Principles of Statistics for the Health Sciences (Spring: 3)**

*Restricted to Connell School of Nursing students.*

This course introduces statistics as a liberal discipline and applies the principles of statistics to problems of interest to health sciences professionals. Students will gain an understanding of statistical ideas and methods, acquire the ability to deal critically with numerical arguments, and gain an understanding of the impact of statistical ideas on the health sciences, public policy and other areas of application.

**MATH 1190 Fundamentals of Mathematics I (Fall: 3)**

**MATH 1191 Fundamentals of Mathematics II (Spring: 3)**

*Restricted to Lynch School of Education and Human Development students.*

**MATH 1190-1191** is a course sequence designed for those who plan to teach mathematics in grades K-8. The emphasis is on building conceptual understanding of the mathematics present in the emerging K-8 curriculum and on deepening content knowledge. Number and number systems through the real number system will be studied; functions and the structure of algebra and geometry will be developed. Problem solving and reasoning, applications, and making connections will be featured.

Be sure to enroll in the Calculus course that's right for your major or program. See our advisement website to help make the right decision.

**MATH 1002-1003 Functions and Differential Calculus (Fall, Spring)**

This course is intended for students who are required to take Calculus I for any major/program but whose backgrounds necessitate additional preparation.

Topics include differential calculus as well as “pre-calculus” material such as the real line and coordinate plane; linear and quadratic functions; higher degree polynomials and rational functions; trigonometry, emphasizing the trigonometric functions; and exponential and logarithmic functions.

Note: Completion of both 1002 and 1003 satisfies the University Core Requirement in Mathematics, as well as any Calculus I requirement.

Department permission is required; see the Assistant Chair for Undergraduates.

**MATH 1100 Calculus I (Fall/Spring: 4)**

**MATH 1100** is a first course in the calculus of one variable intended for Biology, Economics, Management, Psychology / Neuroscience and Premedical students. It is open to others who are qualified and desire a more rigorous mathematics course at the core level.

Students contemplating majors in Chemistry, Computer Science, Geology/Geophysics, Mathematics, or Physics should enroll in MATH 1102 Calculus I for Math and Science Majors, rather than MATH 1100.

Topics include a brief review of polynomials, trigonometric, exponential, and logarithmic functions, followed by discussion of limits, derivatives, and applications of differential calculus to real-world problem areas. A brief introduction to integration may be included at the end of the course.

**MATH 1101 Calculus II (Fall/Spring: 4)**

MATH 1101 is a second course in the calculus of one variable intended for Biology, Economics, Management, Psychology / Neuroscience and Premedical students. It is open to others who are qualified and desire a more rigorous mathematics course at the core level.

MATH 1101 is not open to students who have completed MATH1103. Students contemplating majors in Chemistry, Computer Science, Geology/Geophysics, Mathematics, or Physics should enroll in MATH 1103 Calculus II for Math and Science Majors rather than MATH 1101.

There are three main topics: integration (definition of integration, basic techniques for integration, and select applications); an introduction to differential equations (with applications to population modeling and other contexts); an introduction to multivariable functions and partial derivatives (with application to optimization in economics and other contexts).

**MATH 1102 Calculus I for Math and Science Majors (Fall: 4)**

MATH 1102 is a first course in the calculus of one variable intended for Chemistry, Computer Science, Geology/Geophysics, Mathematics, and Physics majors. It is open to others who are qualified and desire a more rigorous calculus course than MATH 1100.

Topics covered include the algebraic and analytic properties of the real number system, functions, limits, derivatives, and an introduction to integration.

**MATH 1103 Calculus II for Math and Science Majors (Fall/Spring: 4)**

MATH 1103 is a continuation of MATH 1102. Topics covered in the course include several algebraic techniques of integration, many applications of integration, and infinite sequences and series.

**MATH 2202 Multivariable Calculus (Fall/Spring: 4) and MATH 2203 Multivariable Calculus Honors (Fall: 4) **

Prerequisite: MATH 1101, MATH 1103 or equivalent (e.g., five on the BC Calculus Advanced Placement Exam).

This course is for students majoring in Chemistry, Computer Science BS, Geology-Geophysics, Mathematics and Physics as well as other students who have completed integral calculus.

Topics include vectors in two and three dimensions, analytic geometry of three dimensions, parametric curves, partial derivatives, the gradient, optimization in several variables, multiple integration with change of variables across different coordinate systems, line integrals, and Green's Theorem.

Prerequisite: A strong background in single variable calculus, as demonstrated, for example, by a score of 5 on the AP-BC Examination.

MATH 2203 is an honors version of MATH 2202 intended for students with strong preparation and high motivation. Topics covered include vector analysis, partial differentiation, multiple integration, line integrals, Green's theorem, Stokes's theorem, and the Divergence Theorem.

These courses may be required or suggested in certain Schools or Programs.

**MATH 1180 Principles of Statistics for the Health Sciences (Spring: 3)**

*Restricted to Connell School of Nursing students.*

This course introduces statistics as a liberal discipline and applies the principles of statistics to problems of interest to health sciences professionals. Students will gain an understanding of statistical ideas and methods, acquire the ability to deal critically with numerical arguments, and gain an understanding of the impact of statistical ideas on the health sciences, public policy and other areas of application.

**MATH 1190 Fundamentals of Mathematics I (Fall: 3)**

*Restricted to Lynch School of Education and Human Development students. Satisfies Mathematics Core Requirement.*

MATH 1190-1191 is a course sequence designed for those who plan to teach mathematics in grades K-8. The emphasis is on building conceptual understanding of the mathematics present in the emerging K-8 curriculum and on deepening content knowledge. Number and number systems through the real number system will be studied; functions and the structure of algebra will be developed. Problem solving and reasoning, applications, and making connections will be featured.

**MATH 1191 Fundamentals of Mathematics II (Spring: 3)**

*Restricted to Lynch School of Education and Human Development students. Satisfies Mathematics Core Requirement.*

As in MATH 1190, the course emphasizes building conceptual understanding of the mathematics present in the emerging K-8 curriculum and on deepening the content knowledge. Topics drawn from geometry and measurement, data analysis, statistics, and probability will be developed. Problem solving and reasoning, applications, and making connections will be featured.

**MATH 2290 Number Theory for Teachers (Alternate Spring semesters: 3)**

Prerequisites: MATH 1190 and MATH 1191

This course is intended to focus on the wealth of topics that relate specifically to the natural numbers. These will be treated as motivational problems to be used in an activity-oriented approach to mathematics in grades K-9. The course will demonstrate effective ways to use the calculator and computer in mathematics education. Topics include prime number facts and conjectures, magic squares, Pascal's triangle, Fibonacci numbers, modular arithmetic, and mathematical art.

**MATH 2291 Geometry for Teachers (Alternate Spring semesters: 3)**

Prerequisites: MATH 1190 and MATH 1191

This course is intended to fill a basic need of all teachers of grades K-9. Geometry now occupies a significant role in the elementary mathematics curriculum. The course will treat content, but ideas for presenting geometry as an activity-based program will also be stressed. Topics to be covered include the geoboard and other key manipulatives, elements of motion and Euclidean geometry, and suggestions for using Logo as a tool to enhance teaching geometry.

**MATH 4453 Euclid's Elements (Spring: 3)**

Prerequisite: None

This course is a close reading of Euclid's Elements in seminar style, with careful attention to axiomatic reasoning and mathematical constructions that build on one another in a sequence of logical arguments.

We will also emphasize clear and creative communication on mathematical ideas, with some attention to the cultural background of the *Elements* and its place in a modern education.

**MATH 4455 Mathematical Problem Solving (Fall: 3)**

Prerequisites: MATH 2202 Multivariable Calculus, MATH 2210 Linear Algebra, and MATH 2216 Introduction to Abstract Mathematics (or equivalent mathematical background).

Permission of the instructor required for students outside the LSOE.

This course is designed to deepen students' mathematical knowledge through solving, explaining, and extending challenging and interesting problems. Students will work both individually and in groups on problems chosen from polynomials, trigonometry, analytic geometry, pre-calculus, one-variable calculus, probability, and numerical algorithms. The course will emphasize explanations and generalizations rather than formal proofs and abstract properties. Some pedagogical issues, such as composing good problems and expected points of confusion in explaining various topics will come up, but the primary goal is mathematical insight. The course will be of particular use to future secondary math teachers.

#### Required and elective courses for Majors and Minors.

**MATH 2210 Linear Algebra (Fall/Spring: 3)**

Corequisite: MATH 2202/3 Multivariable Calculus

This course is an introduction to the techniques of linear algebra in Euclidean space. Topics covered include matrices, determinants, systems of linear equations, vectors in n-dimensional space, complex numbers, and eigenvalues. The course is required of mathematics majors and minors, but is also suitable for students in the social sciences, natural sciences, and management.

**MATH 2211 Linear Algebra (Honors) (Spring: 3)**

Prerequisite: MATH 2203 Multivariable Calculus (Honors) or permission of the Assistant Chair for Undergraduates

This course is intended for students with strong preparation and high motivation. Topics covered include matrices, linear equations, determinants, eigenvectors and eigenvalues, vector spaces and linear transformations, inner products, and canonical forms. The course will include significant work with proofs.

**MATH 2216 Introduction to Abstract Mathematics (Fall/Spring: 3)**

This course is designed to develop the student's ability to do abstract mathematics through the presentation and development of the basic notions of logic and proof. Topics include elementary set theory, mappings, integers, rings, complex numbers, and polynomials.

**MATH 3310 Introduction to Abstract Algebra (Fall/Spring: 3)**

Prerequisites: MATH 2210 Linear Algebra and MATH 2216 Introduction to Abstract Mathematics.

This course studies four fundamental algebraic structures: groups, including subgroups, cyclic groups, permutation groups, symmetry groups and Lagrange's Theorem; rings, including subrings, integral domains, and unique factorization domains; polynomials, including a discussion of unique factorization and methods for finding roots; fields, introducing the basic ideas of field extensions and ruler and compass constructions.

**MATH 3311 Algebra I (Fall: 3)
MATH 3312 Algebra II (Spring: 3)**

Prerequisites: MATH 2210 Linear Algebra and MATH 2216 Introduction to Abstract Mathematics.

This year-long sequence studies the basic structures of abstract algebra. Topics include groups, subgroups, normal subgroups, factor groups, Lagrange's Theorem, the Sylow Theorems, rings, ideal theory, integral domains, field extensions, and Galois theory.

Note: Students may not take both MATH 3310 and MATH 3311. With the permission of the Assistant Chair for Undergraduates, students who have taken MATH 3310 may be allowed to take MATH 3312. However, they may need to do additional work on their own in order to make that transition. Students considering a B.S. in Mathematics are strongly encouraged to take MATH 3311.

**MATH 3320 Introduction to Analysis (Fall/Spring: 3)**

Prerequisites: MATH 2202 Multivariable Calculus and MATH 2216 Introduction to Abstract Mathematics*.*

The purpose of this course is to give students the theoretical foundations for the topics taught in MATH 1102-1103. It will cover algebraic and order properties of the real numbers, the least upper bound axiom, limits, continuity, differentiation, the Riemann integral, sequences, and series. Definitions and proofs will be stressed throughout the course.

**MATH 3321 Analysis I (Fall: 3)
MATH 3322 Analysis II (Spring: 3)**

Prerequisites: MATH 2210 Linear Algebra and MATH 2216 Introduction to Abstract Mathematics.

This year-long sequence studies the basic structure of the real numbers. Topics include the least upper bound principle, compactness of closed intervals (the Heine-Borel theorem), sequences, convergence, the Bolzano-Weierstrass theorem, continuous functions, boundedness and intermediate value theorems, uniform continuity, differentiable functions, the mean value theorem, construction of the Riemann integral, the fundamental theorem of calculus, sequences and series of functions, uniform convergence, the Weierstrass approximation theorem, special functions (exponential and trig), and Fourier series. As time permits, other topics may include metric spaces, calculus of functions of several variables, and an introduction to measure and integration.

Note: Students may not take both MATH 3320 and MATH 3321. With the permission of the Assistant Chair for Undergraduates, students who have taken MATH 3320 may be allowed to take MATH 3322. However, they may need to do additional work on their own in order to make that transition. Students considering a B.S. in Mathematics are strongly encouraged to take MATH 3321.

**MATH 4410 Differential Equations (Fall; sometimes Spring: 3)**

Prerequisites: MATH 2202 Multivariable Calculus and MT 210 Linear Algebra.

This course is a junior-senior elective intended primarily for the student who is interested in seeing applications of mathematics.

Among the topics covered will be the following: first order linear equations, higher order linear equations with constant coefficients, linear systems, Laplace transforms, and other topics as time permits.

**MATH 4412 Partial Differential Equations (Offered Occasionally: 3)**

Prerequisite: MATH 4410 Differential Equations.

This course investigates the classical partial differential equations of applied mathematics (diffusion, Laplace/Poisson, and wave) and their methods of solution (separation of variables, Fourier series, transforms, Green's functions, and eigenvalue applications). Additional topics will be included as time permits.

**MATH 4414 Numerical Analysis (Spring: 3)**

Prerequisites: MATH 2202 Multivariable Calculus, and MATH 2210 Linear Algebra.

Topics include the solution of linear and nonlinear algebraic equations, interpolation, numerical differentiation and integration, numerical solution of ordinary differential equations, approximation theory.

**MATH 4426 Probability (Fall/Spring: 3)**

Prerequisites: MATH 2202 Multivariable Calculus and familiarity with using a computer.

This course provides a general introduction to modern probability theory.

Topics include probability spaces, discrete and continuous random variables, joint and conditional distributions, mathematical expectation, the central limit theorem, and the weak law of large numbers. Applications to real data will be stressed, and we will use the computer to explore many concepts.

**MATH 4427 Mathematical Statistics (sometimes Fall; Spring: 3)**

Prerequisites: MT 426 Probability and familiarity with using a computer.

Topics studied include the following: sampling distributions, parametric point and interval estimation, hypothesis testing, goodness-of-fit, parametric and nonparametric two-sample analysis. Applications to real data will be stressed, and the computer will be used to explore concepts and analyze data.

**MATH 4430 Introduction to Number Theory (Spring: 3)**

Prerequisite: MATH 2216 Introduction to Abstract Mathematics.

Topics covered include divisibility, unique factorization, congruences, number-theoretic functions, primitive roots, diophantine equations, continued fractions, quadratic residues, and the distribution of primes. An attempt will be made to provide historical background for various problems and to provide examples useful in the secondary school curriculum.

**MATH 4435 Mathematical Programming (Fall: 3)**

Prerequisite: MATH 2210 Linear Algebra.

Topics studied from linear programming include a general discussion of linear optimization models, the theory and development of the simplex algorithm, degeneracy, duality, sensitivity analysis, and the dual simplex algorithm. Integer programming problems, and the transportation and assignment problems are considered,and algorithms are developed for their resolution.

**MATH 4440 Dynamical Systems (Offered Occasionally: 3)**

Prerequisites: MATH 2202 Multivariable Calculus, MATH 2210 Linear Algebra, and MATH 2216 Introduction to Abstract Mathematics.

This course is an introduction to nonlinear dynamics and their applications, emphasizing qualitative methods for differential equations.

Topics include fixed and periodic points, stability, linearization, parameterized families and bifurcations, and existence and nonexistence theorems for closed orbits in the plane. The final part of the course is an introduction to chaotic systems and fractals, including the Lorenz system and the quadratic map.

**MATH 4445 Combinatorics (Fall: 3)**

Prerequisites: MT 216 Introduction to Abstract Mathematics and MT 210 Linear Algebra. MT 210 may be taken simultaneously.

This course is an introduction to graph theory and combinatorics, with a strong emphasis on creative problem-solving techniques and connections with other branches of mathematics. Topics will center around the following: enumeration, Hamiltonian and Eulerian cycles, extremal graph theory, planarity, matching, colorability, Ramsey theory, hypergraphs, combinatorial geometry, and applications of linear algebra, probability, polynomials, and topology to combinatorics.

**MATH 4450 Advanced Linear Algebra (Offered Occasionally: 3)**

Prerequisites: MATH 2210 Linear Algebra and MATH 3310 Introduction to Abstract Algebra.

This proof-based course presents a more rigorous approach to Linear Algebra and covers many topics beyond those in MATH 2210. Topics will include Abstract Vector Spaces and Linear Maps over any field, Modules, Canonical Forms and the Geometry of Bilinear Forms. Additional topics, if time permits, could include the basic theorems of Galois Theory, Matrix Factorization, and applications such as Coding Theory, Factor Analysis and Linear Difference Equations.

**MATH 4451 Euclidean and Non-Euclidean Geometry (Fall: 3)**

Prerequisite: MATH 2216 Introduction to Abstract Mathematics.

This course is an introduction to geometric structure, broadly construed.

Topics may include: Euclidean geometry, hyperbolic and spherical geometry, platonic solids, tilings and wallpaper groups, graph theory, finite geometries, projective geometry, equidecomposition, the isoperimetric problem, surfaces and 3-dimensional manifolds.

**MATH 4453 Euclid's Elements (Spring: 3)**

Prerequisites: None

This course is a close reading of Euclid's Elements in seminar style, with careful attention to axiomatic reasoning and mathematical constructions that build on one another in a sequence of logical arguments.

We will also emphasize clear and creative communication on mathematical ideas, with some attention to the cultural background of the Elements and its place in a modern education.

**MATH 4455 Mathematical Problem Solving (Spring: 3)**

Prerequisites: MATH 2202 Multivariable Calculus, MATH 2210 Linear Algebra, and MATH 2216 Introduction to Abstract Mathematics (or equivalent mathematical background). Permission of the instructor required for students outside the LSOE.

This course is designed to deepen students' mathematical knowledge through solving, explaining, and extending challenging and interesting problems. Students will work both individually and in groups on problems chosen from polynomials, trigonometry, analytic geometry, pre-calculus, one-variable calculus, probability, and numerical algorithms. The course will emphasize explanations and generalizations rather than formal proofs and abstract properties. Some pedagogical issues, such as composing good problems and expected points of confusion in explaining various topics will come up, but the primary goal is mathematical insight. The course will be of particular use to future secondary math teachers.

**MATH 4460 Complex Variables (Fall/Spring: 3)**

Prerequisite: MATH 2202 Multivariable Calculus, and at least one of MATH 2210 Linear Algebra or MATH 2216 Introduction to Abstract Mathematics. Not open to MA students.

This course gives an introduction to the theory of functions of a complex variable, a fundamental and central area of mathematics. It is intended for mathematics majors and minors, and science majors.

Topics covered include: complex numbers and their properties, analytic functions and the Cauchy-Riemann equations, the logarithm and other elementary functions of a complex variable, integration of complex functions, the Cauchy integral theorem and its consequences, power series representation of analytic functions, the residue theorem and applications to definite integrals.

**MATH 4461 Stochastic Processes (Spring: 3)**

Prerequisites : MATH 2216 and MATH 4426

A stochastic process describes the evolution of a system that changes over time in a random manner. This course introduces and studies various properties of some fundamental stochastic processes, including Markov chains in discrete and continuous time, renewal processes, and Brownian motion.

**MATH 4470 Mathematical Modeling (Fall: 3)**

Prerequisites: MATH 2202 Multivariable Calculus and MATH 2210 Linear Algebra.

This is a course primarily for mathematics majors with the purpose of introducing the student to the creation, use and analysis of a variety of mathematical models and to reinforce and deepen the mathematical and logical skills required of modelers.

A secondary purpose is to develop a sense of the existing and potential roles of both small and large scale models in our scientific civilization. It proceeds through the study of the model-building process, examination of exemplary models, and individual and group efforts to build or refine models through a succession of problem sets, laboratory exercises, and field work.

**MATH 4475 The History of Mathematics (Alternate Fall semesters: 3)**

Prerequisites: MATH 3310 and MATH 3320, one of which may be taken concurrently. Students must be familiar with abstract algebra (groups, rings, fields...) and rigorous analysis (differentiation and integration of real valued functions, sequences and series of functions...).

This course studies the development of mathematical thought, from ancient times to the twentieth century. Naturally, the subject is much too large for a single semester, so we will concentrate on the major themes and on the contributions of the greatest mathematicians. The emphasis in the course will be on the mathematics. Students will follow the historical arguments and work with the tools and techniques of the period being studied.

**MATH 4480 Topics in Mathematics (Offered Occasionally: 3)**

Topics for this one-semester course vary from year to year according to the interests of faculty and students. With department permission it may be repeated.

**MATH 4499 Readings and Research (Fall/Spring: 3)**

Department permission is required.

This is an independent study course, taken by arrangement with and under the supervision of a Mathematics Department faculty member.