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Course Descriptions for the BS in Mathematics

16 credits of required courses:

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 include: limits, continuity, derivatives, applications of derivatives, integrals, and the fundamental theorem of calculus. Prerequisite: MATH 162
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 include: techniques of integration, further applications of derivatives, and applications of integration. Prerequisite: MATH 281
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 include: limits, continuity, derivatives, applications of derivatives, integrals, and the fundamental theorem of calculus. Prerequisite: MATH 286
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 Rn together with its bases, linear transformations, and eigenvectors and eigenvalues. Prerequisite: MATH 282

Students in the Mathematics Track must complete:

20 credits of required courses:

Discrete mathematics, the mathematical 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. (Same as CS 272) Prerequisite: MATH 162
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. Prerequisite: MATH 282, MATH 283 recommended but not required.
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. Prerequisite: MATH 283
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: 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

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 CS 495 Software Development (or CS 425 Software Engineering) 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, students will prepare a written paper describing their findings and relating them to principles of the Science of Consciousness. They will also 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. Prerequisite: consent of the Department of Mathematics faculty.

Plus 12 credits of courses at the level of Math 267 or above, including at least one of Math 424: Analysis 2 and Math 432: Algebra 2.

In their final year, students in the Mathematics Track are required to take the Educational Testing Service’s Major Fields Test in Mathematics and submit their results to the Department of Mathematics. This is usually done during the course MATH 490.

Students in the Mathematics and Computer Science Track must complete:

28 credits of required courses:

Discrete mathematics, the mathematical 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. (Same as CS 272) Prerequisite: MATH 162
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. Prerequisite: MATH 282, MATH 283 recommended but not required.
This course covers programming in Java, specifically focusing on object-oriented concepts and creating GUI applications. Topics include: classes and objects, primitives and references, inheritance and polymorphism, interfaces and abstract classes, exception handling, GUI programming in Swing, and serialization and file I/O. Prerequisite: CS 201
This course presents the fundamental principles of object-oriented programming. Students will learn how to write reusable and better-maintained software, and integrate this knowledge with laboratory assignments and projects. Topics include: fundamental principles and models of object-oriented programming, UML class diagrams and design principles that promote reusability and maintainability of software. Prerequisite: CS 221 or equivalent
In this course, students participate in a comprehensive system development project to apply and integrate the concepts of software design and implementation. Topics include: methods and tools for large system development including analysis, design, testing, and documentation. Students work in teams to develop a substantial analysis and design project. Prerequisites: CS 221 and at least one CS 400 level elective

In this course students create an original software project from the ground up from the initial analysis and design phases through implementation and testing. Students are expected to submit several project proposals before the start of the course, and submit a written project postmortem at the end of the course. With Faculty approval this course can be extended to two months to facilitate a larger project. Prerequisite: CS 495 or CS 425

Plus 4 credits of computer science coursework at the level of CS 300 or above and an additional 4 credits of 400 level computer science coursework.

In their final year, students in the Mathematics and Computer Science Track are required to take an assessment test to be chosen by the Department of Mathematics and to submit the results to the Department of Mathematics. Students who take the general Graduate Record Examination (GRE) for entry into graduate school or for other purposes may satisfy this requirement by simply submitting their GRE results to the Department of Mathematics. Students not taking the GRE will need to consult the Department of Mathematics to determine an appropriate test.

Students completing the Mathematics and Computer Science Track are eligible to continue on to MUM’s MS in Computer Science and may be able to complete it in just over a year. Consult the Department of Computer Science for full information.

Students in the Mathematics and Physics Track must complete:

36 credits of required courses:

This course introduces vector calculus. Topics include: gradient, directional derivatives, maxima and minima, curvilinear coordinates, arc length, line integrals. Prerequisite: MATH 283
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. Prerequisite: MATH 283
Classical mechanics provides an accurate description of the objects and phenomena of everyday experience, and constitutes the basis of most of engineering, science, and technology. This course introduces the classical laws governing motion of particles and extended bodies in space and time, beginning with their active formulation in terms of force and acceleration and then deriving the equivalent formulation in terms of conservation of energy, momentum, and angular momentum. Topics include: motion, Newton’s laws, gravitation, and conservation laws. Prerequisite: MATH 281
This course introduces the general principles of fluid mechanics, vibrations and waves. It develops the fundamental principles and mathematical representations of oscillations and standing and traveling waves, as well as conservation of energy and entropy. Topics include: pressure, fluid flow, simple harmonic motion, resonance, mathematical representations of traveling waves, wave properties (such as refraction, diffraction, interference, and polarization), temperature and heat, and the kinetic theory of gases. Prerequisites: MATH 282 and PHYS 210
Electrical forces largely determine the observable properties of matter in the whole range of science from atomic theory to cell biology. The integration of electricity and magnetism constitutes the first unified field theory, anticipating contemporary approaches by more than a century. This course introduces electric and magnetic forces, electric current, and electromagnetic interactions, along with the concepts of electric and magnetic fields and electric potential used to understand and describe them. Topics include: Coulomb’s and Gauss’s laws, the Biot-Savart law and Ampere’s law, Faraday’s law, and Maxwell’s equations. Prerequisites: MATH 282 and PHYS 210
Quantum mechanics and Einstein’s theory of relativity are the major themes of this course. Topics include special relativity, the birth of quantum mechanics, Schrödinger’s equation, wave mechanics of one-dimensional problems, and the hydrogen atom. Prerequisites: MATH 282 and PHYS 210
A survey of classical mechanics.
Topics include: wave mechanics, one-dimensional potential, operator methods and the Dirac formulation, the harmonic oscillator, the classical limit and the WKB approximation. Prerequisites: MATH 282, MATH 286, and PHYS 250; MATH 283 recommended

Students who are completing the Mathematics and Physics Track of the Mathematics Major 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. They will report on readings or research they conduct on a topic or problem suggested by the course PHYS 360 Introduction to Quantum Mechanics. In addition, they will also 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. May be repeated for credit. Prerequisite: consent of the Department of Physics and Department of Mathematics faculty

In their final year, students in the Mathematics and Physics Track are required to take an assessment test to be chosen by the Department of Mathematics and to submit the results to the Department of Mathematics. Students who take the general Graduate Record Examination (GRE) for entry into graduate school or for other purposes may satisfy this requirement by simply submitting their GRE results to the Department of Mathematics. Students not taking the GRE will need to consult the Department of Mathematics to determine an appropriate test.

Electrical forces largely determine the observable properties of matter in the whole range of science from atomic theory to cell biology. The integration of electricity and magnetism constitutes the first unified field theory, anticipating contemporary approaches by more than a century. This course introduces electric and magnetic forces, electric current, and electromagnetic interactions, along with the concepts of electric and magnetic fields and electric potential used to understand and describe them. Topics include: Coulomb’s and Gauss’s laws, the Biot-Savart law and Ampere’s law, Faraday’s law, and Maxwell’s equations. Prerequisites: MATH 282 and PHYS 210

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