32 courses with the subject MATH, each shown exactly as we captured it from the college's catalog, with every element we hold. Where the wording looks broken, that is our reading of the catalog, not the college's text.
MATH 010Problem-Solving
A structured seminar, focusing on problem-solving. Students are encouraged to work collaboratively and individually on challenging mathematical problems that are presented without the context of techniques from a specific course. Problem-solving skills are enhanced, through using higher level thinking and applying techniques to different problem types. Problems in the fall semester include those from past Putnam exam while in the spring semester problems are drawn largely from professional journals. May be repeated for credit. Graded S/U. Three hours per week.
Analytic geometry, the derivative and differential, polynomials, algebraic functions, exponential and logarithmic functions, limits, continuity, and applications. This course is part 1 (of 2) of a yearlong sequence in differential calculus. At the end of this two-course sequence, students will tackle all the topics above included in differential calculus. Completion of this year-long sequence is equivalent to completion of MATH-111. Four hours per week. Four semester hours. (Q, R.) Note: A student who did not place into MATH-111 will be required to take MATH-105 and 106.
This course is the second semester of a year-long sequence in Differential Calculus. Topics in this course include trigonometry, derivatives of trigonometric functions, conic sections, implicit differentiation, and limits at infinity. The semester will conclude with the Fundamental Theorem of Calculus. Completion of this year-long sequence is equivalent to completion of MATH-111. Prerequisite: MATH-105. Four hours per week. Four semester hours.
Limits; derivatives; applications of derivatives; trigonometric, inverse trigonometric, logarithmic, and exponential functions; applications of these functions; indeterminate forms; the Fundamental Theorem of Calculus. Use of a computer algebra system. Prerequisite: Placement based on the high school record and a placement test. Offered both semesters. Four hours per week. Four semester hours. (Q, R.) Note: A student who has received credit for MATH-111 may not enroll in MATH-105 or 106
A continuation of MATH-111 or 105 and 106. Techniques of integration, applications of integration, improper integrals, polar coordinates, parametric equations, infinite sequences and series. Use of a computer algebra system. Prerequisite: Placement based on the high school record and a placement test, or a grade of C- or better in MATH-106, or MATH-111, placement, or permission of instructor. Offered both semesters. Four hours per week. Four semester hours. (Q, R.)
Functions of several variables, including three-dimensional geometry and vectors, space curves and motion in space, partial differentiation, multiple integration, line and surface integrals, and the theorems of Green, Gauss, and Stokes. Use of a computer algebra system. Prerequisite: A grade of C- or better in MATH-112, or permission of the department. Offered both semesters. Four hours per week. Four semester hours. (Q, R.)
Systems of linear equations, matrix algebra, vector spaces, linear transformations, eigenvectors and eigenvalues, inner products and orthogonality, applications. The computer as a computational tool. Prerequisite: MATH-112 or 236W, or permission of the instructor. Offered in the fall semester. Four hours per week. Four semester hours. (R.)
A course designed to bridge the gap between computation-oriented introductory courses and proof-oriented advanced courses. The language of contemporary mathematics, including the proper way to write mathematics, and the nature of mathematical reasoning. Extensive writing projects. Topics studied may include axiomatic systems, logic, set theory, functions, mathematical induction, graph theory and trees, permutations and combinations. Prerequisite: MATH-106, or MATH-111; placement; or permission of the instructor. Offered in the spring semester. Three hours per MATH/PHIL-260. Logic An introduction to the concepts and techniques used in symbolic reasoning, primarily through the study of first-order logic, the translation of sentences of ordinary English into a formal language, and the construction of derivations. Topics include: formalization, proofs, mathematical induction, propositional and predicate logic, quantifiers, and sets. Three hours per week. Four semester hours. (R.)
MATH 310Differential Equations and Mathematical Models
Mathematical methods for developing models in the physical, biological, and social sciences. Emphasis on models involving differential equations. Solutions, visualizations, and interpretations of first order, second order, and systems of linear and non-linear differential equations. Numerical, graphical and analytic methods, with extensive qualitative analysis approaches. Laplace transforms. Independent projects. Additional topics chosen from forcing and resonance, discrete dynamical systems, and power series solutions. Use of a computer algebra system. Prereq
An introduction to the real number system and set operations; theoretical treatment of supremum, infimum, countability, sequences, limits, continuity, and differentiability. Additional topics may include series, structure of point sets and abstract metric spaces. Emphasis on writing mathematical proofs. Prerequisite: MATH-211 and 236W. Offered in the fall semester. Three hours per week. Four semester hours.
A continuation of MATH-311. The Riemann and Riemann-Stieltjes integral; infinite series, sequences and series of functions; introduction to metric spaces. Additional topics may include Lebesgue measure and integration, orthogonal functions and Fourier series. Prerequisite: MATH-311. Offered as needed. Three hours per week. Four semester hours. (R.)
Topics in Euclidean and non-Euclidean geometry, including some of the following: geometry from an axiomatic viewpoint, synthetic Euclidean geometry, transformation geometry and symmetry, affine and projective geometry, inversive geometry, spherical geometry, and hyperbolic geometry. Prerequisites: MATH-235 and 236W, or permission of the instructor. Offered in the spring of odd years. Three hours per week. Four semester hours. (R.)
An introduction to algebraic structures, with emphasis on groups: Subgroups, quotient groups, homomorphisms, isomorphism theorems, Cayley’s theorem, permutation groups. An introduction to the theory of rings. Additional topics may include: series of groups, free groups, and the Sylow theorems. Prerequisites: MATH-235 and 236W. Offered in the spring semester. Three hours per week. Four semester hours.
An introduction to algebraic structures, with emphasis on rings: subrings, ideals, quotient rings, homomorphisms, isomorphism theorems, integral domains, unique factorization domains, Euclidean domains. Additional topics may include: fields and field extensions, Galois theory. Prerequisite: MATH-335. Offered in the fall of odd years. Three hours per week. Four semester hours. (R.)
An introduction to probability theory, discrete and continuous probability distributions, moments and moment-generating functions of random variables, and transformations of random variables. Prerequisite: MATH-211. Offered in the fall semester. Four hours per week. Four semester hours. MATH/STAT-343. Math for Data An introduction to the mathematical foundations of computational data analysis. Topics may include Singular value decomposition, principal component analysis and dimensionality reduction, gradient descent, Markov chains, logistic regression, and classification and clustering as they relate to deep learning and neural nets. Offered in the fall of odd years. Prerequisites: MATH-235 or permission of instructor. Three hours per week. Four semester hours.
A mathematics oral presentation. This course will satisfy the College requirement for an oral presentation in the major. Prerequisite: written consent of a department faculty member. Graded S/U. Zero semester hours. Note: This course is usually taken in conjunction with internships (MATH-381, 383, 384, 441) and research/independent work (MATH-391-394, 441, 491, 492W).
Elements of graph theory, including the study of Eulerian graphs, planar graphs, trees, connectivity, colorings, algorithms, domination, and the applications of graphs to computer science. Prerequisite: MATH-236W. Offered in the fall semester of even years. Three hours per week. Four semester hours.
An academic/work experience under the supervision of an internship adviser and an on-site supervisor. Students must document their experience according to the requirements delineated in the College catalogue section on Internships. An oral presentation to the department is required. Contact the chair of the department for further details. Open to juniors and seniors. The term during which the internship work is performed will be noted by one of the following letters, to be added immediately after the internship course number: A (fall), B (winter), C (spring),
An academic/work experience under the supervision of an internship adviser and an on-site supervisor. Students must document their experience according to the requirements delineated in the College catalogue section on Internships. An oral presentation to the department is required. Contact the chair of the department for further details. Open to juniors and seniors. The term during which the internship work is performed will be noted by one of the following letters, to be added immediately after the internship course number: A (fall), B (winter), C (spring), Note: Students may receive credit for two internships that meet the conditions described in this catalogue.
Independent investigation of an area of mathematics not covered in regular courses. Prerequisite: Written consent of a department faculty member. Graded S/U. One semester hour. Note: This course may be taken more than once.
Independent investigation of an area of mathematics not covered in regular courses. Prerequisite: Written consent of a department faculty member. Graded S/U. Two semester hours. Note: This course may be taken more than once.
Independent investigation of an area of mathematics not covered in regular courses. An oral presentation to the department is required. Prerequisite: Written consent of a department faculty member. Four semester hours. (XLP.) Note: This course may be taken more than once. This course always fulfills the ILE requirement for the college, but may satisfy an elective requirement for the major only with prior permission of the department chair.
Many people today consider mathematics a tool of the physical sciences at best and a pointless exercise in rote memorization at worst. But is there anything more to math than this? Can mathematics contribute to basic human desires such as play, beauty, freedom, justice, and love? Is there any sense in which mathematics can contribute to human flourishing? How does our view of the nature of mathematics affect things like education, personal growth, and human flourishing? This course explores ways in which mathematics can be linked to what it means to be human. Note: MATH-400 does not count as an elective towards the math major or minor. The course does not count towards the (R) college core requirement.
Complex numbers; polar representation; stereographic projection; the exponential and logarithm functions; analytic functions; the Cauchy-Riemann Equations; fractional linear transformations; Cauchy’s integral formula; the theorems of Cauchy, Liouville, Morera, and Goursat; power series expansions; the Residue Theorem. Rouche’s Theorem, the Schwartz Reflection Principle, and the Riemann Mapping Theorem. Prerequisites: MATH-236W and 211. Offered in the spring semester of even years. Three hours per week. Four semester hours.
Selected topics from numerical analysis, which may include systems of linear equations, linear and nonlinear differential equations, numerical integration and differentiation, eigenvalue problems, error analysis, interpolation and approximation. The computer will be used. This course will satisfy the college requirement for a capstone experience in the major. Prerequisite: MATH-211. Offered in the fall semester of even years. Three hours per week. Four semester hours. (R.)
Elementary point set topology; metric spaces; topological spaces, quotient spaces, compactness, and connectedness. Additional topics may include homology or the fundamental group. This course will satisfy the College requirement for a capstone experience in the major. Prerequisite: MATH- 236W. Offered in the spring semester of even years. Three hours per week. Four semester hours.
Divisibility; factorization; distribution of primes; modular arithmetic; Diophantine equations; theorems of Fermat, Euler and Wilson; primitive roots; public-key cryptography, quadratic reciprocity. Additional topics may include: applications to cryptography; digital signatures; algebraic and transcendental numbers; continued fractions; elliptic curves. This course will satisfy the College requirement for a capstone experience in the major. Prerequisite: MATH-236W. Offered in the fall semester of odd years. Three hours per week. Four semester hours.
The mathematical background of modern statistics, including the development of sampling distributions, the theory and application of estimation, tests of hypotheses. This course will satisfy the College requirement for a capstone experience in the major. Prerequisite: MATH-341. Offered in the spring semester. Three hours per week. Four semester hours.
A course designed to acquaint the student with modern trends in advanced topics in mathematics and its applications. The course will be adapted to the students’ preferences and needs. Prerequisite: Permission of the instructor. Three hours per week. Four semester hours. (R.)
A course designed to acquaint the student with modern trends in advanced topics in mathematics and its applications. The course will be adapted to the student’s preferences and needs. Prerequisite: Permission of the instructor. Three hours per week. Four semester hours. (R.)
Independent research in mathematics. This course is appropriate for students pursuing departmental honors and distinguished honors projects, and is open to other students interested in research in mathematics. An oral presentation to the department is required. Prerequisites: Written consent of a member of the faculty to serve as an advisor. Four semester hours. (XLP.) Note: This course may be taken more than once.
Independent research in mathematics. This course serves as the culminating course for departmental honors and distinguished honors projects. This course will satisfy the college requirement for a capstone experience in the major. Prerequisites: MATH-491, meets college and departmental requirements for honors, and written consent of a member of the faculty to serve as an advisor. Four semester hours. (XLP.)
