MATH

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

This course is intended for students who, based on the results of their mathematics assessment and the agreement of the instructor, need to strengthen their quantitative and algebraic skills in order to be ready to progress to further mathematics, science, and economics courses. In this class students learn to translate real problems into mathematics, to solve complex multi-step problems, and to gain confidence in using logarithms, exponents, and trigonometry in different contexts.

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

This course is for students who have not studied calculus and who have the necessary precalculus background. It presents rates of change and their applications, integrals, the fundamental theorem, and modeling of phenomena in the natural and social sciences. All students are required to complete the online self assessment of precalculus skills before the course begins.

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

Topics include techniques of integration, applications of integration, differential equations, sequences, series, and Taylor series.

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

Cryptography is the study of secret communication between different groups of people. From 4,000 years ago in ancient Egypt when secret hieroglyphs were used to communicate the messages of royalty to today when credit card numbers are encrypted to be transmitted over the internet, cryptography has been a necessary part of human life. In this class we will discuss classical cryptography and some historical ciphers along with the mathematical concepts of the modern field. We will study public key cryptography, prime numbers, the discrete logarithm problem, the Diffie-Hellman key exchange, and RSA encryption. If time permits we will also discuss elliptic curve encryption. In particular, we will use the Python programming language and Jupyter notebooks to implement the encryption schemes that we study.

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

Topics include differential and integral calculus of functions of several variables.

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

An introduction to abstract reasoning in the context of real analysis. Topics will be drawn from the real numbers, mathematical induction, functions, sequences, and continuity. The emphasis is on formal mathematical reasoning and writing through proofs.

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

Topics include elements of the theory of matrices and vector spaces.

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

In this course, students will explore the mathematical foundations of interest theory and financial valuation. We will learn how financial mathematics is applied in both business and personal contexts, from valuing financial instruments and portfolio management, to everyday problems such as loan payments and retirement savings. Key topics include interest rate definitions, time value of money, present and accumulated values for various cash flow streams, and pricing and evaluation of financial products. We will also cover how these tools support asset-liability management and risk mitigation. Real-world applications, such as student loans, mortgages, and corporate bonds, will be used throughout the course to illustrate core concepts.

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

Studies some aspects of discrete mathematics. Topics include sets, functions, elementary probability, induction proofs, and recurrence relations.

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

Dynamical systems are mathematical models that evolve with time -- for example, the population of a species in an ecosystem or the price of a financial asset. This course will focus on discrete-time models where one iterates a single variable function and follows the evolution of points in its domain. Our aim will be to study the qualitative, long-term behavior of these models by developing mathematical theory and doing simulation. Topics will include periodicity, bifurcations, chaos, fractals, and computation.

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

A selection of projects with a goal of discovery of properties and patterns in mathematical structures. The choice of projects varies from year to year and is drawn from algebra, analysis, discrete mathematics, geometry, applied mathematics, and statistics.

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

Fall and Spring. Credits: 1 - 4 Restrictions: Contact instructor for independent study declaration form and signatures.Instructor permission required.Notes: The permission of The department is required for independent work to count towards the major or minor.

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

Topics include the real number system, convergence of sequences and series, power series, uniform convergence, compactness and connectedness, continuity, abstract treatment of differential and integral calculus, metric spaces, and point-set topology.

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

Topics include differentiation and integration of functions of a complex variable, the Cauchy integral formula, residues, conformal mapping, and applications to physical science and number theory.

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

Many problems such as calculating the area of a surface, volume of a geometric shape, expected return from an investment and even solutions to differential equations all essentially reduce to being able to "measure" various objects, in other words, integrate various functions. Students in math, statistics, and other fields like economics will often encounter measure-theoretic language in their post-graduate work in academia and in industry. We will primarily focus on the theory of Lebesgue measure on the real line. Some topics may include the extended real number system, outer measure, measurable sets, measurable functions, Lebesgue integration and modes of convergence, and time permitting, abstract measure spaces and L^p spaces.

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

Linear algebra is one of the foundational areas of mathematics. Research from facial recognition and compressed sensing in applied math to deep results in pure math require advanced linear algebra. In addition, computer graphics, large language models, and linear models in statistics rely heavily on linear algebra techniques. Students in this course will learn the abstract mathematical ideas behind these applications, as well as gain experience with computational techniques in the field. Likely topics include abstract vector spaces, inner product spaces, singular value decompositions and other matrix factorizations, numerical techniques, and symmetric matrices.

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

Abstract algebra is the study of the common principles that govern computations with seemingly disparate objects. One way to begin is by studying groups, which are sets with a single operation under which each non-identity element is invertible. Examples include the integers with addition, invertible matrices of size n, permutations of a fixed set, and the symmetries of an object. Our goal is to study a definition of groups that unifies all of the important examples above and more.

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

Abstract algebra is the study of the common principles that govern computations with seemingly disparate objects. One way to begin is by studying rings, which are sets with two operations, typically addition and multiplication. Examples include the integers, the integers modulo n, and polynomials in n variables. Our goal is to study a definition of rings that unifies all of the important examples above and more.

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

Graph theory gives us both an easy way to pictorially represent many major mathematical results and insights into the deep theories behind them. Graphs seem simple -- they're just collections of dots connected by curves -- but are very rich structures that arise naturally in applications ranging from social networks to electric power grids. We will examine properties such as isomorphism, connectivity, planarity, and coloring using classic examples such as paths, cycles, trees, complete graphs, and polyhedral graphs. More advanced topics will be determined by student interest and course trajectory.

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

This course will begin with an introduction to number theory, covering material on congruences, prime numbers, arithmetic functions, primitive roots, quadratic residues, and quadratic fields. We will then continue our study of number theory by picking special topics which might include some of the following: Finite Fields, Prime Factorization of Ideals, Fermat's Last Theorem, Elliptic curves, Dirichlet's Theorem on Arithmetic Progressions, the Prime Number Theorem, or the Riemann Zeta function.

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

This course is an introduction to point-set topology, which is a fundamental language for much of modern mathematics. One of the goals of topology is to understand what it means for a function to be continuous, first in Euclidean space, and then to generalize the notion of continuity to other spaces. The core topics to be studied include: basic set theory, various interesting topologies, continuous functions, connectedness and compactness. Topics from algebraic topology will be covered if time permits.

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

This is an introduction to differential equations for students in the mathematical or other sciences. Topics include first-order equations, second-order linear equations, and qualitative study of dynamical systems

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

Partial differential equations (PDEs) are often used to describe natural phenomena arising in a wide variety of contexts including physics, biology, and economics. Our focus will be on basic yet representative linear partial differential equations such as the heat and wave equations. We will explore the motivation behind each model we study and emphasize methods of finding solutions and analyzing their behavior. Techniques will include transform methods, separation of variables, energy methods, and numerical computations.

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

Mathematical optimization involves finding the best solution to a problem from a set of feasible solutions defined by mathematical constraints. It has an elegant theory and applications in fields like management, economics, engineering, and computer science that require decision making under constraints on time or other resources. We will begin by studying linear optimization, including duality, the simplex algorithm, and the geometry of linear programming. Other topics will include discrete optimization, network optimization, and nonlinear optimization.

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

Stochastic processes are mathematical models that evolve with time and include an element of randomness. They involve a collection of states-for example, the weather in a geographical location, the size of a population, or the length of a queue-and a description of how the system evolves from one state to the next. This course is devoted to the study of a class of stochastic processes called Markov chains, and we attempt to study their behavior using tools from probability theory and linear algebra in beautiful, interconnected ways. Topics will include Markov chains in discrete and continuous time, branching processes, queuing theory, and Markov chain Monte Carlo.

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

This course develops the ideas of probability simultaneously from experimental and theoretical perspectives. The laboratory provides a range of experiences that enhance and sharpen the theoretical approach and, moreover, allows us to observe regularities in complex phenomena and to conjecture theorems. Topics include: introductory experiments; axiomatic probability; random variables, expectation, and variance; discrete distributions; continuous distributions; stochastic processes; functions of random variables; estimation and hypothesis testing.

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu

Fall and Spring. Credits: 1 - 8 Restrictions: Contact instructor for independent study declaration form and signatures.Instructor permission required.Notes: The permission of The department is required for independent work to count towards the major or minor.

Subject

MATH

Type

course

Edition

2026

Source

catalog.mtholyoke.edu