Mathematics (B.S.)
Courses
MATH 200 The Mathematics of Infinity from Small to Super-Large
The course provides a gentle introduction to the modern history of mathematical infinity through the theory of large cardinals (infinities so large they can’t be proven to exist). Students will explore the different levels of infinity, examine for themselves a few of the enormous large cardinals, and discover how Maharishi’s Vedic Mathematics suggests a solution to a modern-day problem about the mathematical infinite – a solution that is the subject of recently published research. The main Prerequisite is a willingness to explore the nature of the Infinite and to learn a new kind of mathematics in the process. (4 credits) Prerequisite: STC 108/109
MATH 205 Maharishi Vedic Mathematics: Mathematical Structure and the Transcendental Source of Natural Law
This course studies the mathematics of Veda, as explained by Maharishi. Topics include mathematical models of the self-referral structure of the Veda, mathematics as the intellectual expression of the structure of pure knowledge, mathematics in the Vedic Literature, and examination of the principles of modern mathematics in the light of Maharishi Vedic Science. (2–4 credits) Prerequisite: STC 108/109
MATH 266 Geometry for the Artist: Applying Abstractions of Shape and Form to Create Beautiful Concrete Images
Geometry, the study of shape and form, is an essential tool for the visual artist. Topics in this course include symmetry, Euclidean and non-Euclidean geometry, perspective and projective geometry, and fractals. Materials fee: $10 (4 credits) Prerequisite: STC 108/109
MATH 267 Geometry: From Point to Infinity — Using Properties of Shape and Form to Handle Visual and Spatial Data
Geometry gives an understanding of shape, form, and structure that has many applications in mathematics, science, and technology. In-depth study of Euclidean and non-Euclidean geometries and their applications. (4 credits) Prerequisite: MATH 162
MATH 272 Discrete Mathematics: Unified Approaches to Managing Discrete Phenomena in Computer Science and Other Disciplines
Discrete mathematics, the study of finite processes and discrete phenomena, is essential for computer science. Topics include logic and sets, relations and functions, vertex-edge graphs, recursion, and combinatorics. (4 credits) Prerequisite: MATH 162
MATH 281 Calculus 1: Derivatives as the Mathematics of Transcending, Used to Handle Changing Quantities
MATH 282 Calculus 2: Integrals as the Mathematics of Unification, Used to Handle Wholeness
MATH 283 Calculus 3: Unified Management of Change in All Possible Directions
Calculus, one of the most useful areas of mathematics, is the study of continuous change. It provides the language and concepts used by modern science to quantify the laws of nature and the numerical techniques through which this knowledge is applied to enrich daily life. Using the mathematics computer laboratory, students gain a clear understanding of the fundamental principles of calculus and how they are applied in real-world situations. (4 credits each)
Topics Calculus 1: limits, continuity, derivatives, applications of derivatives, integrals, and the fundamental theorem of calculus. Prerequisite: MATH 162
Topics Calculus 2: techniques of integration, further applications of derivatives, and applications of integration. Prerequisite: MATH 281
Topics Calculus 3: infinite series, functions of several variables and their derivatives, gradient, directional derivatives, vector-valued functions and their derivatives, the Jacobian matrix, and chain rule. Prerequisite: MATH 286
MATH 286 Linear Algebra 1: Linearity as the Simplest Form of a Quantitative Relationship
Linear algebra studies linearity, the simplest form of quantitative relationship, and provides a basis for the study of many areas of pure and applied mathematics, as well as key applications in the physical, biological, and social sciences. Topics include systems of linear equations, vectors, vector equations, matrices, determinants, vector spaces, bases, and linear transformations. (4 credits) Prerequisite: MATH 282
MATH 304 Calculus 4: Locating Silence within Dynamism
This course extends the calculus of a function of a single real variable to functions of several real variables. Topics include maxima and minima, curvilinear coordinates, line integrals, multiple integrals, change of variables, gradient fields, surface integrals, and the theorems of Green, Stokes, and Gauss. (4 credits) Prerequisite: MATH 283
MATH 307 Linear Algebra 2: Unified Approaches to Linear Transformations
This course deepens and extends many of the topics covered in Linear Algebra 1; additional topics include the Cayley-Hamilton theorem, Jordan canonical form, inner-product spaces, orthogonality, and spectral theory. (4 credits) Prerequisite: MATH 286
MATH 308 Ordinary Differential Equations: Describing Evolving Systems and Predicting Their Future
The most concise mathematical expression that describes a continuously changing physical system is a differential equation, which uses derivatives to quantify all possible states of an evolving system in one equation. Topics include first-order differential equations, second-order linear differential equations, power-series solutions, Laplace transforms, numerical methods of solution, and systems of differential equations. (4 credits) Prerequisite: MATH 283
MATH 310 Mathematical Problem Solving: Systematic Techniques for Using Mathematics to Solve Problems
Problem solving is a fundamental — and exciting — part of mathematics. In this course, students develop and practice many methods and techniques of mathematical problem solving. (4 credits) Prerequisite: MATH 282
MATH 318 Complex Analysis: Transcending the Real Numbers to a Simpler and More Unified Numbering System
Complex analysis is one of the great achievements of modern mathematics, providing an extension of the real number line to a two-dimensional plane of numbers with surprising applications throughout most areas of mathematics. Topics include analytic functions, Cauchy-Riemann equations, contour integration, Cauchy’s Theorem and integral formulas, power series, residue theorem, and conformal mappings. (4 credits) Prerequisite: MATH 304
MATH 351 Probability: Locating Orderly Patterns in Random Events to Predict Future Outcomes
Probability provides precise descriptions of the laws underlying random events, with applications in quantum physics, statistics, computer science, and control theory. Topics include permutations and combinations, conditional probability, random variables, discrete and continuous distributions, expectation, and the central limit theorem. (4 credits) Prerequisite: MATH 282
MATH 353 Probability and Statistics 1: Methods for Deriving Dependable Knowledge from Incomplete Information
Probability provides precise mathematical descriptions of the laws underlying random events, and statistics uses this mathematical theory to make inferences from empirical data and assess their reliability. Topics include probability, random variables, probability distributions, mean and standard deviation, central limit theorem, tests of hypotheses, linear regression, and correlation. (4 credits) Prerequisite: MATH 161
MATH 354 Probability and Statistics 2: Methods for Deriving Dependable Knowledge from Incomplete Information
The topics of Probability and Statistics 1 are studied more deeply, with emphasis on their mathematical foundations. (4 credits) Prerequisites: MATH 353 and MATH 283
MATH 370 Mathematical Logic: Mathematical Criteria for Establishing Accurate Forms of Knowledge
Mathematical logic is the mathematical description of the structure and function of the symbolic language of mathematics. This course develops a rigorous symbolic language, suitable for expressing all mathematical concepts, demonstrates the soundness and completeness of the language, and shows the inherent limitations of such formal systems indicated by Gödel’s Incompleteness Theorems. (4 credits) Prerequisite: consent of the instructor
MATH 401 Practicum in Teaching College Mathematics: Knowledge Is Structured in Consciousness
Under the direction of a senior faculty member, students prepare and give lectures, lead tutorial sessions, and write and grade quizzes and exams for a college-level mathematics course. (4 credits) Prerequisite: consent of the instructor
MATH 402 Undergraduate Research in Mathematics
This course provides an opportunity for students to do original research under the supervision of a faculty member. (1 credit) Prerequisite: consent of the instructor
MATH 410 Seminar in Applied Mathematics 1: Knowledge Is for Action
MATH 411 Seminar in Applied Mathematics 2: Knowledge Is for Action
In these courses, students apply the theoretical knowledge they have gained in previous mathematics courses to an applied problem taken from a real-life situation in business or industry. Problems differ from year to year. (4 credits each — may be repeated) Prerequisite: consent of the instructor
MATH 420 Numerical Analysis: Using Abstract Mathematical Principles to Design Accurate and Efficient Numerical Methods for Solving Problems
Scientific and engineering applications of computers require advanced numerical techniques of manipulating and solving complex systems of equations with great efficiency and minimum error. Topics include numerical solutions of systems of linear equations, curve fitting, interpolation, numerical integration, solution of algebraic equations, and error analysis. (4 credits) Prerequisite: MATH 282
MATH 423 Real Analysis 1: Locating the Finest Impulses of Dynamism within the Continuum of Real Numbers
MATH 424 Real Analysis 2: Developing a Conceptual Foundation for Calculus
Analysis is the mathematically rigorous development of calculus based on the theory of infinite sets. The analysis sequence begins with the application of the infinitary methods of set theory to construct the uncountable continuum of real numbers and unfold its topological structure, and then shows how the basic principles of calculus can be logically unfolded from this set-theoretic understanding of the continuum. (4 credits each)
Topics 1: infinite sets, completeness, open sets, closed sets, compact sets, connected sets, and continuous functions. Prerequisite: MATH 283
Topics 2: properties of continuous functions, differentiation, mean value theorem, Riemann integral, numerical sequences and series. Prerequisite: MATH 423
MATH 431 Algebra 1: Algebraic Operations as the Self-Interacting Dynamics of a Mathematical System
MATH 432 Algebra 2: The Integration and Interaction of Two Algebraic Operations on a Mathematical System
Algebra is the study of the structures given to sets of elements by operations or relations as well as the structure-preserving transformations between these sets. (4 credits each)
Topics Algebra 1: groups and subgroups, quotient groups, group homomorphisms, direct sum, kernel, image, Noether isomorphism theorems, and the structure of finitely generated abelian groups. Prerequisite: MATH 286
Topics Algebra 2: rings, integral domains, fields, principal ideal domains, unique factorization domains, modules and submodules, tensor products, and exact sequences. Prerequisite: MATH 431
MATH 434 Set Theory: Mathematics Unfolding the Path to the Unified Field — the Most Fundamental Field of Natural Law
Set theory provides a unified foundation for the diverse theories of modern mathematics based upon the single concept of a set. Topics include axioms of set theory, ordinals, transfinite induction, the universe of sets, cardinal arithmetic, large cardinals, and independence results. (4 credits) Prerequisite: MATH 370
MATH 436 Foundations of Mathematics: The Unified Field as the Basis of All of Mathematics and All Laws of Nature
This course introduces recent developments that have provided important new insights into the structure of the foundations of mathematics. Topics covered in the course vary from year to year. (4 credits) Prerequisite: MATH 370
MATH 460 Topics in Set Theory
Topics vary from year to year and may include large cardinals and elementary embeddings; applications of set theory to topology and analysis; applications of set theory to algebra; introduction to the theory of forcing; Gödel’s constructible universe; descriptive set theory. (4 credits) Prerequisite: consent of instructor
MATH 466 Topology: Relation between Point and Infinity
Topology shows how all mathematical aspects of shape, structure, and form can be expressed in terms of set theory. Students study topologies and their properties of separation, connectedness and compactness, topological mappings, and the fundamental group of a topological space. (4 credits) Prerequisites: MATH 423 and 431
MATH 485 Theory of Computation: The Laws That Govern the Self-Interacting Dynamics of Numbers and Their Application
Students focus on formal abstract models of computation and capabilities of abstract machines in relation to their increasing ability to recognize more general classes of formal languages. Topics include formal grammars, finite-state machines, equivalence of finite-state machines, right-linear and left-linear grammars, pushdown automata, context-free languages, Turing machines, unsolvable problems, and recursive functions. (4 credits) Prerequisite: MATH
MATH 490: Senior Project: Integration of All Knowledge in the Self
Students write a substantial paper unifying the knowledge gained from the courses taken during their major and relating this knowledge to deep principles from Maharishi’s Vedic Science. This paper may take the form of: 1) An integrated summary of main ideas from the courses taken during their major, addressing themes and questions to be provided by the Department of Mathematics, or 2) A paper written in accord with the guidelines for submissions for the Raja Raam Award and submitted for that award (see description elsewhere in this Catalog), or 3) A report of research conducted by the student on a mathematical topic or problem chosen in conjunction with the Department of Mathematics. In all of these cases, the paper will be made by the student into a poster for submission for presentation at the annual Knowledge Celebration in June of the year of completion of the major. (4 credits) Prerequisite: consent of the instructor
The content of this page was reviewed in January 2010.
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