Mathematics
(413) 662-5369
Chairperson: Elizabeth Hartung, Ph.D.
Email: E.Hartung@mcla.edu
Mathematics Major
The Department of Mathematics offers a four-year program leading to a Bachelor of Science in mathematics. The program fosters insights and solutions to a variety of problems through symbolic and numerical analysis. The practice of the discipline requires and engenders precise modes of thinking. The use of calculus, numerical methods, probability, statistics, and logic is basic to the quantitative methods needed throughout society today.
Students graduating with a major in Mathematics will be able to:
- Perform computations and procedures from a wide range of the various branches of mathematics;
- Demonstrate mathematical growth by acquiring a solid grasp of key concepts and themes;
- Develop fluency in reading and constructing mathematical proofs;
- Apply mathematical ideas and problem-solving to real-life situations in the various disciplines.
Mathematics Courses
MATH 100 Math for Educators I3 cr
Reviews key concepts in numbers, operations, and algebra. Examines proofs and explanations suitable for elementary instruction. Covers: number bases other than ten, the order of operations, and the addition, subtraction, multiplication, and division of integers, fractions, and algebraic expressions.
MATH 101 Math for Educators II3 cr
Reviews key concepts in functions, algebra, and geometry. Examines proofs and explanations suitable for elementary instruction. Covers: decimals, percents, exponents, radicals, functions, sequences, equations, dimensional analysis, and basic geometry, including angles, areas, volumes, and basic proofs.
Prerequisite: MATH 100
MATH 102 Mathematics for Liberal Arts3 cr
Reviews fundamental concepts of arithmetic, algebra, and geometry. Surveys basic statistics and financial mathematics. Students will practice computational skills and information literacy for discerning truth and problem solving.
Attributes: Quantitative Reasoning (CMA)
MATH 150 Precalculus3 cr
Introduces topics necessary for the study of calculus. A detailed study of algebraic, trigonometric, exponential and logarithmic functions and equations, and their applications to modeling real world problems. Topics are considered from analytical, graphical and numerical points of view.
Prerequisite: Placement based on SAT scores and high school background
Attributes: Quantitative Reasoning (CMA)
MATH 201 Math Modeling for Educators3 cr
Explores the tools necessary to create and adapt mathematical modelling projects suitable for K-12 mathematics students. Reviews current best practices in assessment and transparency, with a focus on writing and coding in mathematics. Students will create a final modelling project suitable for direct inclusion in a classroom setting, with lesson plans, assignment templates, rubrics, and plans for giving appropriate support and feedback.
MATH 202 Math Seminar1 cr
Explores the discipline of mathematics in order to support majors in their academic work and help them understand their career options. Introduces the diversity of fields within mathematics through presentations, reading and writing activities and interactions with peers and mentors. This seminar is required for all MCLA math majors.
Repeatable: Maximum of 3 credits
MATH 220 Calculus I3 cr
Examines limits, continuity, the derivative, differentiation of elementary functions, applications of the derivative and an introduction to the antiderivative. The first of a four-part sequence.
Prerequisite: MATH 150, placement based on SAT scores, high school background or department approval
Attributes: Quantitative Reasoning (CMA)
MATH 230 Calling Bullshit3 cr
Teaches students how to recognize persuasion, trickery, or lies that show a blatant disregard for facts and the truth - in a word bullshit. Because it is not enough in today's world to simply recognize bullshit when it appears in its myriad forms, students will also learn how to counter bullshit in powerful and persuasive ways, enhancing not only their own information literacy in the process, but that of people they encounter when they call bullshit.
MATH 232 Introduction to Statistics3 cr
Examines descriptive statistics, probability, discrete and continuous random variables, sampling theory, confidence intervals, and hypothesis testing from inferential statistics. Includes the binomial distribution, normal distribution, and t-distribution.
Attributes: Quantitative Reasoning (CMA)
MATH 232E Introduction to Statistics - Enhanced4 cr
Examines descriptive statistics, probability, discrete and continuous random variables, sampling theory, confidence intervals, and hypothesis testing from inferential statistics. Includes the binomial distribution, normal distribution, and t-distribution. The enhanced 4-credit version of MATH 232 will provide students extra time and instructor guidance. This additional time will include reviewing relevant pre-requisite material and working on practice problems together with the instructor.
Attributes: Quantitative Reasoning (CMA)
MATH 232H Honors: Introduction to Statistics3 cr
Examines descriptive statistics, probability, discrete and continuous random variables, sampling theory, confidence intervals, and hypothesis testing from inferential statistics. Includes the binomial distribution, normal distribution, and t-distribution.
Attributes: Quantitative Reasoning (CMA), Honors Program (HONR)
MATH 240 Proof I3 cr
Introduces sets, Boolean logic, combinatorics, functions, and the basics of mathematical proof.
Prerequisite: Completion of Tier I Quantitative Reasoning requirements or instructor approval
MATH 250 Discrete Mathematics3 cr
Provides a foundation in mathematical topics central to the study of computer science, emphasizing mathematical reasoning and algorithms. Topics include propositional logic, Boolean algebra, mathematical proofs and induction, computer arithmetic, elementary combinatorics, recursion, graphs and trees, matrices, sequences and summation.
MATH 261 Linear Algebra3 cr
Investigates vector spaces, linear equations, linear transformations, determinants, inner product spaces, eigenvalues and eigenvectors.
MATH 270 Statistics and Data Analysis4 cr
Examines descriptive statistics, probability, discrete and continuous random variables, confidence intervals, hypothesis testing, analysis of variance, regression and correlation. Includes normal distribution, t-distribution, chi square distribution. Required computer programming laboratory.
Corequisite: MATH 270L
Attributes: Quantitative Reasoning (CMA)
MATH 286 Topics in Mathematics1-4 cr
Examines sophomore level topics in mathematics that complement departmental offerings in mathematics or math competency courses. Emphasis is on the nature of mathematical thought and applications of mathematics.
Prerequisite: Completion of Tier I Quantitative Reasoning requirements or instructor approval
Repeatable: Unlimited Credits
MATH 301 Math for Middle and High School Educators3 cr
Provides in-depth explanations for the mathematics taught in middle and high school: algebra, equations, and functions. Covers methods for providing differentiated instruction - reviewing topics from arithmetic (fractions, numbers, and operations) while simultaneously introducing new topics.
Prerequisite: Completion of Tier I Quantitative Reasoning requirements
MATH 310 Proof II3 cr
Examines a wide variety of proof techniques (e.g. direct, by contradiction, by contrapositive, bi-directional, uniqueness, by induction, by counter-example). Students will practice these techniques and learn how and when to apply each one. Functions and relations will provide many examples, and be covered in-depth.
Prerequisite: MATH 240
MATH 320 Calculus II3 cr
Studies antiderivatives, the definite integral, transcendental functions, techniques and applications of integration, an introduction to improper integrals. The second of a four-part sequence.
Prerequisite: MATH 220
MATH 330 Calculus III3 cr
Studies infinite series, plane curves, polar coordinates, vectors, vector-valued functions and analytic geometry in three-dimensional space. The third of a four-part sequence.
Prerequisite: MATH 320
MATH 331 Probability and Statistics I3 cr
Examines probability laws, discrete and continuous random variables and their probability distributions, expectation, moments and moment generating functions, sequences of random variables and Markov chains.
MATH 332 Probability and Statistics II3 cr
Examines functions of random variables, sampling distribution, limit theorems, estimation, hypotheses testing, linear regression, correlation, analysis of variance and analysis of enumerative data.
Prerequisite: MATH 331
MATH 340 Graph Theory3 cr
Investigates definitions and examples of graphs, graph isomorphism, paths and circuits, connectivity, trees, planar graphs, Euler's formula, graph coloring, four and five color theorems and applications.
Prerequisite: MATH 240
MATH 340H Honors: Graph Theory3 cr
Investigates definitions and examples of graphs, graph isomorphism, paths and circuits, connectivity, trees, planar graphs, Euler's formula, graph coloring, four and five color theorems and applications.
Prerequisite: MATH 240
Attributes: Honors Program (HONR)
MATH 344 Geometry3 cr
Studies geometries from an advanced standpoint. Some of the topics that may be covered are non-Euclidean geometry, geometry of the complex plane, affine geometry or projective geometry.
Prerequisite: MATH 310
MATH 345 Game Theory3 cr
Introduces game theory terminology, zero-sum, two-person games, minimax theorem, optimal mixed strategies and applications to economics.
Prerequisite: MATH 261
MATH 360 Number Theory3 cr
Introduces the basic concepts of number theory: the Euclidean algorithm, primes, divisibility theorems, Mersenne and Fermat numbers, linear Diophantine equations, congruences, unique factorization and quadratic reciprocity.
MATH 362 Abstract Algebra3 cr
Introduces the study of algebraic structures with a detailed examination of groups, their properties, and their mappings, including both isomorphic and homomorphic mappings. Cyclic, symmetric, and quotient groups will be studied, as well as groups of permutations, cosets, and normal subgroups. Also covers the Fundamental Homomorphism Theorem.
Prerequisite: MATH 310
MATH 365 Mathematical Modeling3 cr
Explores the development of mathematical models that solve different types of problems, including both discrete and continuous real-world problems that are either deterministic or probabilistic. Determines solutions analytically and through the use of mathematical software.
MATH 372 History of Mathematics3 cr
Examines the historical development of mathematics and its impact from ancient to modern times.
Prerequisite: MATH 320
MATH 380 Differential Equations3 cr
Examines first- and second-order differential equations with particular emphasis on nth order equations with constant coefficients, differential operators, systems of equations, series solutions, and Laplace transforms.
Prerequisite: MATH 330
MATH 390 Numerical Analysis3 cr
Studies the approximation of polynomials at points and over intervals; numerical solutions of algebraic and transcendental equations in one unknown using geometric and arithmetic methods; numerical differentiation; and integration.
MATH 430 Calculus IV3 cr
Concludes the four-semester sequence of calculus with the study of functions in two or more variables, their derivatives and partial derivatives, multiple integrals, line and surface integrals, Green's Theorem and Stoke's Theorem.
Prerequisite: MATH 330
MATH 440 Topology3 cr
Covers various topological spaces. Continuity, connectedness, and compactness are analyzed and compared. Applications of continuity will be applied to the contraction mapping principle. Analysis of product spaces and quotient spaces. Alternate topics may be discussed.
Prerequisite: MATH 310
MATH 444 Operations Research3 cr
Covers various interrelated topics such as linear programming, network analysis, game theory, probability and queuing theory, and optimization theory.
Prerequisite: MATH 430
MATH 455 Complex Variables3 cr
Studies the basic theory of functions of a complex variable including complex numbers and their algebra; analytic functions; Cauchy-Riemann conditions; and the differential and integral calculus of analytic functions.
Prerequisite: MATH 430
MATH 460 Real Analysis3 cr
Examines the basis of calculus with a rigorous exploration of the function concept from both a set-theoretic and topological viewpoint with particular attention to the completeness of the real number system, limits, continuity and convergence of sequences and series.
MATH 486 Special Topics in Mathematics1-4 cr
Introduces theory that is an extension of various upper-division mathematics courses. Special topics may explore, but are not restricted to: analysis, geometry and theory related to modern technology.
Prerequisite: Varies by course
Repeatable: Unlimited Credits
MATH 500 Independent Study1-3 cr
Open to juniors and seniors who wish to read in a given area or to study a topic in depth. Written reports and frequent conferences with the advisor are required.
Prerequisite: Junior status, department approval
Repeatable: Maximum of 12 credits
MATH 540 Internship in Mathematics1-15 cr
Qualified students may be placed as interns in mathematically oriented positions. The internship is designed to supplement and apply classroom study.
Prerequisite: Junior status, department approval
Repeatable: Maximum of 15 credits
MATHEMATICS: TEACHER LICENSURE
Students majoring in mathematics may choose to pursue initial teacher licensure as an early childhood teacher or elementary teacher. Also, mathematics majors may pursue initial licensure as a teacher of mathematics for the middle school or secondary levels. Students seeking any of these licenses must complete a mathematics major and a licensure program in education.