**Locating the Basis of Mathematics in the Self-Interacting Dynamics of Consciousness**

Arithmetic is the study of patterns, relations, and operations on numbers. Topics include the arithmetic of integers, fractions, decimal fractions, ratios, and percents, with an emphasis on applications. (0 credits)

**Using Variables to Manage All Possible Numbers at the Same Time and Solve Practical Problems**

The infinitely flexible language of algebra is used to quantify and model mathematical patterns and relationships. Topics include operations on algebraic expressions, linear equations, the coordinate plane, inequalities, factoring, and simple quadratic equations. (4 credits) *Prerequisite: *Math 051

**Using Variables to Manage All Possible Numbers at the Same Time and Solve Practical Problems**

This course extends Elementary Algebra to develop further algebraic models. Topics include polynomials, rational and radical expressions, quadratic equations, and graphing in the coordinate plane. (4 credits) *Prerequisite: *MATH 152

**Name and Form — Locating the Patterns of Orderliness That Connect a Function with Its Graph and Describe Numerical Relationships**

A mathematical function quantifies the relationship between two related quantities and can be used to model change. Functions and their graphs are essential to all branches of mathematics and their applications. Topics: domain and range, average rate of change, graphs, functions (linear, exponential, logarithmic, and quadratic), and applications. (4 credits) *Prerequisite: *MATH 153

**Name and Form — Learning to Relate the Shape of a Graph to Its Corresponding Function**

A mathematical function quantifies the relationship between two related quantities and can be used to model change. Functions and their graphs are essential to all branches of mathematics and their applications. Topics: trigonometry, algebra of functions, compositions and inverses of functions, functions (trigonometric, power, polynomial, and rational), and applications. (4 credits) *Prerequisite: *MATH 161

**Knowledge is for Action**

This course is designed especially for students entering the major in Sustainable Living who do not have the basic algebraic prerequisites for that major. Topics are drawn from college algebra, geometry, functions, and graphs, and these topics are related to problems in Sustainable Living such as landscaping, heat loss, solar and wind energy, and water management. (4 credits) *Prerequisite: *MATH 152

**Exploring the Full Range of Mathematics and Seeing Its Source in Your Self**

Mathematics takes place in the imagination, in consciousness, unlimited either by finite measuring instruments, by the senses, or even by the feelings. At the same time, mathematics has strict criteria for right knowledge. The power of mathematics lies in bringing infinity out into the finite and making it useful in everyday life — from deciding which bank offers the best return on money, to medical imaging, to designing textiles, to creating a work of art, to putting a man on the moon. In this course, students explore many different ways in which mathematics expresses, emerges from, and uses infinity and its self-interacting dynamics. They look at the foundation of mathematics in the infinitary processes of set theory, the universe of sets, different sizes of infinity, the continuum and its limit process, sequences and series, infinite replication, and applications of infinity in many areas of life. (4 credits)

**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)

**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

**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) *Prerequisites: *MATH 162, (WTG 192 recommended)

**Derivatives as the Mathematics of Transcending, Used to Handle Changing Quantities**

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. Topics: limits, continuity, derivatives, applications of derivatives, integrals, and the fundamental theorem of calculus. (4 credits) *Prerequisite: *MATH 162

**Integrals as the Mathematics of Unification, Used to Handle Wholeness**

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. Topics: techniques of integration, further applications of derivatives, and applications of integration. (4 credits) *Prerequisite: *MATH 281

**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. Topics: infinite series, functions of several variables and their derivatives, gradient, directional derivatives, vector-valued functions and their derivatives, the Jacobian matrix, and chain rule. (4 credits) *Prerequisite: *MATH 286

**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

**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

**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

**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

In this course students investigate a specialized area of mathematics in depth. Topics will vary. (4 credits — may be repeated for credit) *Prerequisite: *consent of the instructor

**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

**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

**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

**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

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

**Locating the Finest Impulses of Dynamism within the Continuum of Real Numbers**

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. Topics: infinite sets, completeness, numerical sequences and series, open sets, closed sets, compact sets, connected sets, and continuous functions. (4 credits) *Prerequisite: *MATH 283

**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. Topics: properties of continuous functions, differentiation, mean value theorem, Riemann integral. (4 credits) *Prerequisite: *MATH 423

**Algebraic Operations as the Self-Interacting Dynamics of 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. Topics: groups and subgroups, quotient groups, group homomorphisms, direct sum, kernel, image, Noether isomorphism theorems, and the structure of finitely generated abelian groups. (4 credits) *Prerequisite: *MATH

**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. Topics: rings, integral domains, fields, principal ideal domains, unique factorization domains, modules and submodules, tensor products, and exact sequences. (4 credits) *Prerequisite: *MATH 431

**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

**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

**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 272

**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 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 integrating the 40 Aspects of the Vedic Literature and Rajaraam’s discoveries to mathematics. They may relate mathematics to the 40 Aspects of the Vedic Literature as Rajaraam has done for physiology in his book “Human Physiology: Expression of the Veda” and “Ramayan in Human Physiology”, or they may explore the significance and consequences of Rajaraam’s discoveries for mathematics, 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 May of the year of completion of the major. (4 credits) Prerequisite: consent of the instructor