**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, including geometry. Instruction consists of a combination of computer software and classroom activities.

(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 models and equations, the coordinate plane, inequalities, factoring, and simple quadratic equations. Instruction consists of a combination of computer software and classroom activities.

(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 quadratic equations, polynomials, rational and radical expressions and equations, and graphing in the coordinate plane. Instruction consists of a combination of computer software and classroom activities.

(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 include 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 include 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, trigonometry, 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 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) No prerequisite

**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) No prerequisite

**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. Topics include an 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. 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. 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 include infinite series, functions of several variables, partial derivatives, gradient, directional derivatives, and the chain rule.

(4 credits) Prerequisite: MATH 286

**Linearity as the Simplest Form of a Quantitative Relationship**

Linear algebra is the study of 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, vector equations, matrices, the vector space R_{n} together with its bases, linear transformations, and eigenvectors and eigenvalues.

(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, multiple integrals, change of variables, arc length, and line integrals.

(4 credits) Prerequisite: MATH 283

**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, 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 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, axiomatic definition of probability, conditional probability, random variables, discrete and continuous distributions, expectation and variance, and the central limit theorem.

(4 credits) Prerequisite: MATH 282

**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 include 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 2 continues the mathematically rigorous development of calculus based on the theory of infinite sets. Topics include properties of continuous functions, differentiation, sequences and series of functions, 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 286

**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 include 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

**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.

For students in the Mathematics Track of the Mathematics Major, this paper is a report of readings or research conducted by students on a topic or problem suggested by the two course sequence Math 423–424 Real Analysis or Math 431–432 Abstract Algebra, taken by students in their final year.

Students in the Mathematics and Computer Science Track of the Mathematics Major replace this course with the two courses CS 495 Software Development and CS 496 Senior Project, in which they will write a program for a particular application. Students in the Mathematics and Physics Track of the Mathematics Major replace this course with the course PHYS 490 Senior Project, in which they report on readings or research they conduct on a topic or problem suggested by the course PHYS 360 Introduction to Quantum Mechanics. In all these cases, the student will prepare an oral presentation, suitable for a lay audience, based on the paper, for submission for presentation at the annual Knowledge Celebration in June of the year of completion of the major.

(4 credits, may be repeated for credit) Prerequisite: consent of the instructor

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