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This course is intended for those students who do not plan to take Calculus but who wish to take a mathematics course for general interest or to fulfill an area requirement. The course is designed to illustrate the applications of a variety of mathematical tools, including set theory, linear equations and inequalities, matrices, linear programming, probability, statistics, and game theory.
Prerequisites: High school plane geometry and higher algebra.
Offered Fall and Spring semesters
MCS 120 Pre-Calculus Mathematics (1 course)
Topics include logic, sets, number systems, equations, inequalities, functions, exponential and logarithmic functions, trigonometric functions.
Prerequisites: High school plane geometry and higher
algebra.
Offered Fall and Spring semesters.
MCS 121 Calculus I (1 course , QUANT)
Introduction to the basic ideas of differential and integral calculus and formal development of differentiation and integration.
Prerequisites: Two years of high school mathematics beyond
plane geometry, including trigonometry, or MCS120.
Offered Fall and Spring semesters.
MCS 122 Calculus II (1 course , QUANT)
A continuation of Calculus I. Topics to be covered include: techniques and applications of integration, polar coordinates, parametric equations, an introduction to and the uses of infinite series, including power series and Taylor series, the basics of ordinary differential equations.
Prerequisite: MCS121 or MCS131
Offered Fall and Spring semesters.
MCS 132 Honors Calculus II (1 course , QUANT)
Same topics as MCS 122, but the approach is more rigorous, emphasizing not only the standard finished results of calculus but also the foundational items and reasoning patterns leading to these results.
Prerequisite: Admission by consent of instructor
Offered Fall semester.
MCS 140 Elementary Statistics (1 course, QUANT)
Survey of uses of statistics, organization of data, observation and measurement, averages, variability, association, probability, randomness, sampling distributions, estimation, tests of hypotheses, and introduction to design. Students with a calculus background who want statistics should take MCS142 or MCS341, MCS342.
Prerequisite: Course in higher algebra or consent of
instructor.
Offered Fall and Spring semesters
MCS 142 Introduction to Statistics (1 course, QUANT)
Gathering, organizing and describing data, probability, random variables, sampling distributions, estimation, hypothesis testing, linear regression, and analysis of variance. Treatment is more mathematical than MCS 140, but the emphasis is still on applications. Introduction to the use of computerized statistical packages. Students who have already taken a statistics course may not earn credit for MCS142.
Prerequisite: MCS121 or MCS131
Offered Fall and Spring semesters.
MCS 170 Computers and Society (1 course)
This is a survey course designed for non-computer science students who desire a general introduction to what a computer is, the history of mechanical computation and computing machinery, and how computers are used as a tool in a variety of disciplines and settings. Emphasis will be placed on uses of the computer in business, industry and research, the social and natural sciences, the humanities, medicine, government, and the home. Students will receive a limited amount of hands-on experience with word processors, data management systems, and both statistical and graphics packages. Other topics to be covered include single-user vs. time-shared systems, programming vs. use of available software, privacy and the computer, robotics, data communication, computer crime, the future of computer technology, and artificial intelligence.
Note: This course is not a prerequisite for any
course in computer science; credit will not be given to students who
have completed MCS177 or any higher numbered computer science
course. This course will not meet distributional requirements for any
curriculum.
Offered occasionally
MCS 177 Introduction to Computer Science I (1 course , QUANT)
An introduction to the perspectives and methods of computer science, especially abstraction, the process of hiding specifics irrelevant to the purpose at hand. Students will learn how to express general procedural ideas and how to use general categories of data in terms of their operational properties. They will also learn the relationship between the form of a procedure and that of the computational process it generates, including the resource consumption of that process. Additionally, students will learn how to prove that a procedure has the desired effect, and why such proofs are not always possible. The course will also address the history of computer science and its relationship with mathematics; problems of computer crime, privacy, and reliability; and the role computation has played as a metaphor for intelligence and social phenomena.
Offered Fall and Spring semesters.
MCS 178 Introduction to Computer Science II (1 course)
A continuation of MCS 177. Students will learn how to model systems using abstractions of state and information flow. They will also learn how to use programming language definition as an abstraction mechanism, and how to implement a newly defined language by writing an interpreter in an existing language. Finally, they will concretely implement computational abstractions by designing computing machines and implementing programming languages using them.
Prerequisites: MCS177
Offered Fall and Spring semesters.
MCS 200 Mathematical Problem Solving (.5 course)
Students will work together on interesting non-routine mathematical problems, few of which will require advanced techniques. This is not a lecture course, and the faculty advisor will serve mainly as a discussion leader. The group will discuss and practice mental attitudes leading to successful problem solving. In the Fall semester, students participate in the national Putnam Mathematics Competition. In the Spring semester, students prepare for the actuarial exams.
Offered Fall Semester
MCS 220 Introduction to Analysis: Theory of the Calculus (1 course)
This course in introductory analysis develops the logical foundations underlying the calculus of real-valued functions of a single variable. Many of the topics from MCS 121 and MCS 122 are treated here, but now from a more advanced standpoint. Accordingly, students also will be introduced to the methodology of mathematics, that is, how to create convincing proofs of mathematical statements. Topics include axioms of the reals, sequences and series of real numbers and functions, limits, uniform continuity and convergence, differentiation, integration, the Mean Value Theorem, and the Fundamental Theorem of the Calculus.
Prerequisites: MCS122 or MCS132
Offered Fall and Spring semesters.
MCS 221 Linear Algebra (1 course)
An introduction to the theory and applications of linear algebra. Topics include vector spaces and linear transformations, matrices and linear transformations, determinants, eigenvalues and eigenvectors, and inner product spaces.
Offered Fall and Spring Semesters.
MCS 222 Multivariable Calculus (1 course)
A multidimensional look at topics from MCS 121 and MCS 122, including functions of several variables, curves and surfaces in Euclidean n-space, standard coordinate systems, partial differentiation (including numerical approximation, the implicit and inverse function theorems), multiple integration (including Stokes' and Green's theorems).
Fall and Spring Semester
MCS 236 Relation-Based Structures (1 course)
This course introduces relation-based structures such as graphs, trees, and lattices, and introduces the student to techniques for proving mathematical theorems.
Offered Fall and Spring semesters
MCS 242 Applied Statistical Methods (1 course)
This is a second course in statistics. The focus is the application of statistical methods to practical problems involving real data from many disciplines. Topics to be covered include regression analysis, experimental design and analysis of variance, and time series analysis. In addition, students will learn to use a statistical software package.
Spring Semester of even numbered years
MCS 250 Operations Research (1 course)
A survey of operations research with emphasis on linear programming and its special applications. Topics discussed will include linear model development, the simplex and revised simplex algorithms, sensitivity analysis, inventory and transportation problems, network techniques, dynamic programming, and queueing theory.
Offered occasionally
MCS 253 Differential Equations (1 course)
First and second order ordinary differential equations, higher-order differential equations, existence and uniqueness theorems, applications of first and second order differential equations, series solutions, numerical methods, systems of ordinary differential equations, an introduction to partial differential equations including classical examples and the separation of variables technique.
Spring Semesters
MCS 256 Discrete Mathematics (1 course)
This course introduces basic notions of discrete structures, such as graphs, networks, and trees; it presents modes of reasoning that aid in the logical analysis of possibilities in large finite structures. Just as calculus treats continuous models and their problems, this course treats discrete mathematical models and related problems. This subject matter is of special interest in computer science.
Spring Semester
MCS 265 The Theory of Computation (1 course)
This course covers the theoretical underpinnings of modern computer science. Topics include automata, nondeterminism, grammars, Turing machines, the halting problem, unsolvability and computational complexity.
Spring Semester
MCS 268 Career Exploration, Internship (Course value varies)
Off-campus employment experience related to the student's major. See description of the Internship Program. Credit toward major or minor will be given only upon departmental approval.
Prerequisite: Junior or Senior status
Fall and Spring Semesters, and Summer
MCS 270 Object-Oriented Software Development (1 course)
This course builds skills directly relevant to real-world software development. Students learn the basics of object-oriented analysis, design, and programming. They also gain experience with techniques for quality assurance, group and project coordination, and documentation in the context of a substantial group project.
Prerequisites: MCS178.
Offered Spring semester.
MCS 284 Introduction to Computer Organization (1 course)
Representation, storage, and processing of digital information; levels of organization of a computer, from the digital logic level to the machine language level; processors, memories, and input/output; introduction to assembly language programming and laboratory study of a particular microprocessor.
Fall Semester
MCS 287 Organization and Theory of Programming Languages (1 course)
A study of the underlying mathematical theory of programming languages combined with a survey of the different types of languages and the basic principles of language structure and design.
Spring Semester
MCS 291, 391 Independent Study (Course value varies)
Fall and Spring semesters and January Term
MCS 303 Geometry (1 course)
Selected topics from logical systems and basic laws of reasoning, foundations of Euclidean geometry, finite geometries, geometric loci, transformations, inversion, non-Euclidean geometry, hyperbolic plane geometry, projective geometry, affine geometry, and computer geometry.
Fall Semester
MCS 313 Modern Algebra (1 course)
An intensive study of the basics of abstract algebra, including the theory of groups, rings, and fields. Topics include permutation and cyclic groups, Lagrange's Theorem, homomorphisms and isomorphisms, normal subgroups and factor groups, integral domains, ideals and factor rings, polynomial rings, factorization of polynomials, and extension fields.
Fall and Spring Semesters of even numbered years
MCS 314 Modern Algebra II (1 course)
A continuation of MCS 313, Modern Algebra I. Topics to be covered include unique factorization domains, principal ideal domains, Euclidean domains, finite fields, constructibility, the fundamentals of Galois theory, and the Sylow theorems.
Spring Semester in odd numbered years
MCS 321 Elementary Theory of Complex Variables (1 course)
Derivative and integral of a function of a complex variable, Cauchy's integral theorem and formula, calculus of residues, application to evaluation of integrals, conformal mappings, and various other topics as indicated by the interests, needs, and experiences of the students.
Spring Semester
MCS 331 Real Analysis (1 course)
An introduction to the techniques and theorems of real analysis. Topics will include: metric spaces and real function theory, including Riemann-Stieltjes integration and sequences and series of functions.
Fall Semester
MCS 332 Topology (1 course)
An introduction to the techniques and theorems of basic point-set topology. Topics will include: countability and separation axioms, Urysohn's Lemma, compactness, connectedness and product spaces. Optional topics may be covered from other areas in analysis and topology.
Spring Semester of even numbered years
MCS 341 Probability Theory and Mathematical Statistics I (1 course)
The probability model, random variables, conditional probability and independence, probability functions, density functions, expectation, some important discrete and continuous distributions, the central limit theorem.
Fall Semester of even numbered years
MCS 342 Probability Theory and Mathematical Statistics II (1 course)
Normal, chi-square, t, and F distributions. Principles of statistical estimation and hypothesis testing. Non-parametric methods. Regression, correlation, and analysis of variance.
Spring Semester of odd numbered years
MCS 344 Topics in Advanced Mathematics (1 course)
An investigation into a branch of mathematics not covered elsewhere in the curriculum. The topic will change from year to year, depending on the interests of instructors and students. Examples of possible areas of study include differential geometry, topology, history of mathematics, partial differential equations, Banach space theory, algebraic geometry, number theory.
Spring Semester of odd numbered years
MCS 350 Honors Thesis (1 course)
To receive credit for this course, a student must complete an approved honors theses fulfilling the requirements of the Mathematics Honors Program or the Computer Science Honors Program. Guidelines are published in the Mathematics and Computer Science Advising Guides, which are available from the department secretary.
Offered on demand
MCS 353 Applied Analysis (1 course)
A study of applied analytical techniques and ideas that are used in a wide range of cognate subjects related to mathematics. Topics will include: partial differential equations, including separation of variables, characteristics and the specific study of the heat and wave equations; special functions and how they arise in physical systems; initial and boundary value problems and Sturm-Liouville theory; transformations, including Fourier and Laplace transforms, and their applications. Optional topics may include one or more of the following topics: qualitative theory of differential equations, the theory of distributions, or the calculus of variations.
Fall Semester
MCS 355 Numerical Analysis (1 course)
A survey of numerical analysis with topics including source and propagation of error, root-finding for nonlinear equations, polynomial approximation, interpolation, finite difference equations, numerical integration, numerical methods for differential equations, and numerical methods for matrices.
Spring Semester of odd numbered years
MCS 358 Mathematical Model Building (1 course)
An introductory study of the formulation of mathematical models to represent, predict and control real-world situations, especially in the social and biological sciences. The course will use ideas from calculus, linear algebra, and probability theory to describe processes that change in time in some regular manner, which may be deterministic or stochastic. Typical topics are Markov and Poisson processes, discrete and continuous equations of growth, and computer simulation. In addition, students will work on their own mathematical modeling projects.
January Term even numbered years
MCS 375 Algorithms: Analysis and Design (1 course)
This course introduces many of the fundamental ideas and techniques necessary for the further study of computer science. Topics include elementary data structures, the divide-and-conquer method, the greedy method, dynamic programming, basic search and traversal techniques, back-tracking, branch-and-bound, NP-hard and NP-complete problems.
Fall Semester
MCS 378 Operating Systems (1 course)
Computer operating system principles, and the inter- relationships between the operating system and the architecture of computer systems. Topics will include dynamic storage allocation, memory and process management, recovery procedures, resource allocation, and concurrency issues. Programming will be done in C.
Fall Semester
MCS 385 Principles of Artificial Intelligence (1 course)
We will critically examine the underlying issues of artificial intelligence. The basic question is: to what extent is computation a fruitful model of intelligence? This course will involve reading primary source materials, participating in group discussions, and writing essays and computer programs in Scheme.
Spring Semester of odd numbered years
MCS 388 Compiler Design (1 course)
An in-depth theoretical study of compiler design. Topics covered include: finite state grammars and recognizers, lexical scanners, context-free languages and context-free parsing techniques, code generation and syntax-directed translation schema.
Spring Semester
MCS 394 Topics in Computer Science (1 course)
Advanced topics in computer science, such as database management systems, language structures, compiler construction, advanced numerical analysis, automata theory and computability theory.
Spring Semester of even numbered years
MCS 391, MCS 291 Independent Study (Course value varies)
Fall and Spring semesters and January Term
MCS 399 Mathematics Seminar (0 course)
Strongly recommended for all mathematics and computer science majors. Different topics will be covered each semester under a seminar format of mutual investigation and discussion. Students will be exposed to special subjects not covered in other courses.
Fall and Spring Semesters