# Mathematics (MATH)

**MATH-100 Precalculus
**

*Instructor permission required.*

**MATH-100QR Precalculus: 'Problem Solving and Quantitative Reasoning'
**

*Fall. **Credits: 4*

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.

*Applies to requirement(s): Meets No Distribution Requirement**D. Shepardson**Instructor permission required.**Advisory: Permission of instructor. Send score from math online self-assessment and background information to dshepard@mtholyoke.edu*

**MATH-101 Calculus I
**

*Fall and Spring. **Credits: 4*

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.

*Applies to requirement(s): Math Sciences**P. Rosnick, J. Tirrell*

**MATH-102 Calculus II
**

*Fall and Spring. **Credits: 4*

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

*Applies to requirement(s): Math Sciences**T. Chumley, T. Shelly*

**MATH-112 History of Mathematics
**

**MATH-114 Explorations in Number Theory
**

*Spring. **Credits: 4*

We will cover the arithmetic of whole numbers and of prime numbers, in particular, examining some of the earliest questions in mathematics from a modern perspective, finding whole number solutions to equations with several variables, deciding whether or not such solutions exist and if so, determining whether the solution set is finite or infinite. Topics include the theory of 'finite arithmetic,' converting questions about the infinite set of whole numbers to those involving just a small set of primes, using computers to examine problems numerically.

*Applies to requirement(s): Math Sciences**G. Davidoff**Advisory: a good grasp of arithmetic*

**MATH-120 Explorations in Geometry
**

**MATH-158EX Developing Mathematical Ideas: Examining Features of Shape
**

*Not Scheduled for This Year. **Credits: 2*

Participants examine aspects of 2-dimensional and 3-dimensional shapes, develop geometric vocabulary, and explore both definitions and properties of geometric objects. The seminar includes a study of angle, similarity,congruence, and the relationships between 3-dimensional objects and their 2-dimensional representations. Participants examine how students develop these concepts through analyzing print and video cases as well as reading and discussing research articles.

*Crosslisted as: X.MATH-402**Applies to requirement(s): Meets No Distribution Requirement**A. O'Reilly, S. Smith**Instructor permission required.**Notes: Half semester.*

**MATH-158ME Developing Mathematical Ideas: Measuring Space in One, Two, and Three Dimensions
**

*Not Scheduled for This Year. **Credits: 2*

Participants examine aspects of 2-dimensional and 3-dimensional shapes, develop geometric vocabulary, and explore both definitions and properties of geometric objects. The seminar includes a study of angle, similarity,congruence, and the relationships between 3-dimensional objects and their 2-dimensional representations. Participants examine how students develop these concepts through analyzing print and video cases as well as reading and discussing research articles.

*Crosslisted as: X.MATH-405**Applies to requirement(s): Meets No Distribution Requirement**A. O'Reilly, S. Smith**Instructor permission required.**Notes: Half semester.*

**MATH-203 Calculus III
**

*Fall and Spring. **Credits: 4*

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

*Applies to requirement(s): Math Sciences**A. Hoyer-Leitzel, M. Robinson, J. Sidman**Prereq: MATH-102 or its equivalent. *

**MATH-211 Linear Algebra
**

*Fall and Spring. **Credits: 4*

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

*Applies to requirement(s): Math Sciences**T. Chumley A. Hoyer-Leitzel, D. Shepardson, J. Sidman**Prereq: MATH-102 or above. *

**MATH-232 Discrete Mathematics
**

*Fall and Spring. **Credits: 4*

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

*Applies to requirement(s): Math Sciences**G. Davidoff, A. Hoyer-Leitzel, M. Robinson, D. Shepardson, J. Tirrell**Prereq: MATH-102 or above or COMSC-101. *

**MATH-251 Mathematical Experimentation: An Introduction to Research in the Mathematical Sciences
**

*Spring. **Credits: 4*

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.

*Applies to requirement(s): Math Sciences**Other Attribute(s): Writing-Intensive**J. Tirrell**Prereq: MATH-102 or above. *

**MATH-295 Independent Study
**

*Fall and Spring. **Credits: 1 - 4*

*The department**Instructor permission required.**Notes: The permission of The department is required for independent work to count towards the major or minor.*

**MATH-301 Real Analysis
**

*Spring. **Credits: 4*

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.

*Applies to requirement(s): Math Sciences**D. Shepardson**Prereq: MATH-102, MATH-211, and MATH-232. *

**MATH-302 Complex Analysis
**

*Fall. **Credits: 4*

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.

*Applies to requirement(s): Math Sciences**G. Davidoff**Prereq: MATH-203 and MATH-301 or Intro to Math Methods (PHYS-303/PHYS-200/PHYS-205). **Notes: offered alternate years at Mount Holyoke and Smith Colleges*

**MATH-309 Topics in Analysis
**

**MATH-311 Abstract Algebra
**

*Fall. **Credits: 4*

Topics include algebraic structures: groups, rings (including some elementary number theory), fields, and vector spaces.

*Applies to requirement(s): Math Sciences**G. Davidoff, M. Robinson**Prereq: MATH-211 and MATH-232. *

**MATH-319 Topics in Algebra
**

**MATH-327 Advanced Logic
**

*Not Scheduled for This Year. **Credits: 4*

This course uses the predicate calculus to present a careful development of formal elementary number theory, and elementary recursion theory, culminating in a proof of Gdel's incompleteness results. It includes some discussion of the philosophical significance of these results for the foundations of mathematics.

*Crosslisted as: PHIL-327**Applies to requirement(s): Humanities**S. Mitchell**Prereq: PHIL-225. *

**MATH-329 Topics in Geometry
**

**MATH-329TP Topics in Geometry and Topology: 'Topology'
**

*Spring. **Credits: 4*

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.

*Applies to requirement(s): Math Sciences**J. Sidman**Prereq: MATH-232 and any 300-level math class. *

**MATH-333 Differential Equations
**

*Spring. **Credits: 4*

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

*Applies to requirement(s): Math Sciences**A. Hoyer-Leitzel**Prereq: MATH-211. *

**MATH-339 Topics in Applied Mathematics
**

**MATH-339PT Topics in Applied Mathematics: 'Optimization'
**

*Not Scheduled for This Year. **Credits: 4*

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.

*Applies to requirement(s): Math Sciences**D. Shepardson**Prereq: MATH-211. *

**MATH-339SP Topics in Applied Mathematics: 'Stochastic Processes'
**

*Spring. **Credits: 4*

A stochastic process is a collection of random variables. For example, the daily prices of a particular stock are a stochastic process. Topics of this course will include Markov chains, queueing theory, the Poisson process, and Brownian motion. In addition to theory, the course will investigate applications of stochastic processes, including models of call centers and models of stock prices. Simulations of stochastic processes will also be used to compare with the theory.

*Crosslisted as: STAT-334SP**Applies to requirement(s): Math Sciences**T. Chumley**Prereq: MATH-211 and MATH-342. *

**MATH-342 Probability
**

*Fall. **Credits: 4*

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.

*Applies to requirement(s): Math Sciences**T. Chumley**Prereq: MATH-203. *

**MATH-395 Independent Study
**

*Fall and Spring. **Credits: 1 - 8*

*The department**Instructor permission required.**Notes: The permission of The department is required for independent work to count towards the major or minor.*