Basic Mathematics for Science
Students will develop mastery of basic mathematical skills and concepts, with a particular emphasis on those skills most needed for introductory science courses. Graded Pass/Fail. 0.5 unit. Not open to students with prior credit in MAT113 or MAT121 or above. Does not count toward the major or minor.
Calculus with Review I
A two-course sequence including a review of algebra, trigonometry, and analytic geometry integrated with an introduction to the theory of differential and integral calculus. Completion of 111 satisfies the Abstraction and Formal Reasoning LADR.
A review of the precalculus topics which are essential for success in Calculus: inequalities; equations and their graphs; functions (polynomial, rational, trigonometric, exponential, and logarithmic). Includes an introduction to the concepts of limit, tangent line slope, and area beneath a curve. Does not count toward a major or minor in Mathematics. Prerequisite: MAT 101, placement at the Ready for Precalculus level, or concurrent enrollment in MAT101.
An introduction to the theory of differential and integral calculus for functions of one variable. Includes the concepts of limit, continuity, derivatives, and indefinite integrals and definite integrals, culminating in the Fundamental Theorem of Calculus. Applications to related rates and optimization problems. Recommended: A strong background in algebra and trigonometry, or 113. Students are advised to take the departmental placement exam to assess their proficiency in algebra and trigonometry. Partially satisfies the SM CCR and satisfies the QL ACE. Prerequisite: MAT 113, or placement at the Ready for Calculus level
Differentiation and integration of logarithmic functions, exponential functions, and inverse trigonometric functions. Study of polar coordinates, conic sections, and various integration techniques. Applications to computations of volumes, surface areas, and centers of mass. Prerequisite: 121 or equivalent college course, or placement via departmental placement test. Partially satisfies the SM CCR and satisfies the QL ACE.
Math Topics for Liberal Arts
Non-technical introduction to selected concepts of modern mathematics (such as logic, set theory, axiomatic systems, non-Euclidean geometry, number theory, graph theory, etc.) that illustrate the nature of mathematics and its connections to other areas of knowledge. Does not count toward major or minor. Partially satisfies the SM CCR and satisfies the QL ACE.
Mathematics for Elementary Teachers
A study of mathematical concepts that are taught in elementary school, including problem solving, sets, numbers and their properties, operations on sets and numbers, geometry, measurements, probability and statistics. Does not count toward a major or minor in math. Prerequisite: EDU 221. Partially satisfies the SM CCR.
Use of graphs and numerical summaries to describe data from individual variables and to investigate relationships among variables. Design of statistical experiments. Survey of fundamental concepts of probability, including sampling distributions. Use of sample data to estimate, and to test hypotheses about, unknown parameters. Does not count toward major. No prerequisites. Partially satisfies the SM CCR and satisfies the QL ACE.
Logic, Sets and Relations
An introduction to the foundations of mathematics, with emphasis on developing basic reasoning skills needed for constructing proofs. Required for major. Counts toward minor but not in addition to Mat 243. Partially satisfies the SM CCR.
Differentiation and integration of vector-valued functions. Study of functions of several variables, including partial derivatives and multiple integrals. Detailed study of infinite sequences and series. Prerequisite: 122 or equivalent. Satisfies the Abstraction and Formal Reasoning LADR.
Systems of linear equations and their solutions. Study of the algebraic properties and applications of vectors, matrices, and linear transformations. Prerequisite: 121.
Survey of basic techniques for describing dynamical systems by means of equations involving derivatives of functions, and of methods for finding functions which satisfy these equations. Prerequisite: 122.
Discrete Mathematics I
A survey of the math topics which are foundational to computer science: functions, relations, sets, basic logic, proof techniques, combinatorics, graphs and trees, discrete probability. Prerequisite MAT 101 MAT 113, MAT 121 (or above), or placement at the Ready for Precalculus level or above, or concurrent enrollment in MAT 101. Partially satisfies the SM CCR.
History of Mathematics
Survey of important discoveries in mathematics and the historical contexts in which they were made. Topics will include major mathematical developments beginning with the Ancient Greeks and tracing the development through Hindu, Arabic and European mathematics up to the modern developments of the 20th century. Prerequisite: 121 or permission.
Introduction to Number Theory
Explores properties of the integers such as divisibility and congruence, linear diophantine equations, prime numbers, the Fundamental Theorem of Arithmetic, Fermat's little theorem, Euler's Theorem, Euler's phi function, computing powers and roots in modular arithmetic, and public key cryptography. Prerequisite: Mat 243 or 220.
Introduction to Real Analysis
Development of the algebraic and topological properties of the real number system and the theoretical foundations of differential and integral calculus. Prerequisite: 221. Strongly recommended for students considering post- graduate study in mathematics.
Introduction to Complex Analysis
Study of complex numbers and functions of a complex variable. Topics include algebra and geometry of the complex plane, derivatives, integrals, power series, Laurent series, and residue theory. Prerequisite: 221 or permission. Recommended for students considering graduate study in mathematics.
Study of concepts abstracted from algebraic properties of the classical number systems, including groups, rings, fields, order relations, and equivalence relations. Prerequisite: 220 or 243.
Probability & Statistics
Calculus-based survey, including axioms of probability, discrete and continuous random variables, standard probability functions (binomial, normal, Poisson, etc.), mathematical expectation, generating functions, and a brief introduction to estimation and hypothesis testing. Prerequisite: 122.
Foundations of Geometry
Survey of ancient, classical and modern views regarding the nature of space, the description of spatial structures and the organization of facts about space into deductive theories. Prerequisite: 121.
Discrete Mathematics II
Continues the discussion of discrete mathematics introduced in Mat 243. Topics include predicate logic, recurrence relations, graphs, trees, matrices, computational complexity, elementary computability and discrete probability. Prerequisite: 243 or 220.
Introduction to Topology
Study of concepts, growing out of and underlying geometry and calculus, which have become important in physics, chemistry, logic, and computer science. Careful development of abstract notions such as topological spaces, continuity, topological equivalence, connectedness, and dimension, and related philosophical and historical matters in mathematics and liberal arts generally. Prerequisite: 121.
Rings and Fields
Selected topics, including rings, subrings, integral domains, fields, ideals, quotient rings, ring homomorphisms, polynomial rings, extension fields, finite fields. Prerequisite: 324. Recommended for students considering graduate study in mathematics.
Content varies. Prerequisite: 327. Offered on demand.
Student-led inquiry/research in an area of mathematics such as real or complex analysis, topology, algebra, etc. Content varies. May be repeated for credit. Prerequisite: Open to junior and senior math majors.