The Major in Mathematics provides a foundation in mathematics, plus electives in mathematics, computer science, biology, and/or physics. The program allows for flexibility in student goals by providing two tracks within the major.

The Mathematics Track provides a strong foundation in mathematics up to the level of a two-course sequence in either abstract algebra or real analysis. It includes a senior project in one of these areas or a related area.

- Students are prepared for graduate study in mathematics or for a career in a technical, professional, or scientific area.
- By careful selection of additional courses, students may graduate prepared to undertake graduate study in computer science, in business, or in other professional and scientific areas. This includes the opportunity to complete the Master of Science in Computer Science at UMLAC in just over a year.
- By also majoring in education, students can graduate prepared to teach mathematics in primary or secondary schools.

Before entering the Mathematics Track of the Major in Mathematics, students must successfully complete Functions and Graphs 2 (MATH 162). It is highly recommended that students also complete College Composition 2 (WTG 192).

Math 162 is equivalent to a Pre-calculus course or a course in College Algebra with Trigonometry. To satisfy this requirement, students take a placement test in mathematics. Depending on where they are placed, they complete at MUM any courses leading up to and including Math 162. This requirement is not satisfied by transfer credit, as the knowledge needs to be current.

In addition to the requirements below for the BS in Mathematics, students need to satisfy the general requirements for a bachelor’s degree.

Students in all tracks of the math major must complete:

- MATH 281 Calculus 1
- MATH 282 Calculus 2
- MATH 283 Calculus 3
- MATH 286 Linear Algebra 1

Students in the Mathematics Track must also complete:

- MATH 272 Discrete Mathematics
- MATH 351 Probability
- MATH 423 Real Analysis 1
- MATH 431 Abstract Algebra 1
- MATH 490 Senior Project

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

The Program Learning Outcomes for the Mathematics Track of the Mathematics Major are given below.

The main measures used to evaluate the success of the Program and locate any areas of concern can be found in the Program Assessment Measures.

**Knowledge: We aim to produce individuals who**

- K1. Understand mathematical concepts and theory, are able to apply them in various fields, and relate them to principles of Maharishi Vedic Science.
- K2. Appreciate the full range of mathematics from its deepest foundational levels, to its expressions in algebra, analysis, and geometry, to its applications in all areas of human endeavor.
- K3. Have a working knowledge of the elements of single and multivariable calculus, discrete mathematics, linear algebra, probability, abstract algebra, and real analysis.

**Skills: We aim to produce individuals who are able to**

- S1. Solve problems creatively in mathematics and its applications.
- S2. Use good number sense to decide whether answers are in the right ball park (orders of magnitude, rules of thumb), are meaningful (rounded appropriately, accuracy, extraneous roots, etc.), and are correct (checking answers when possible).
- S3. Construct rigorous proofs of mathematical theorems at the level of abstract algebra and elementary real analysis. Justify answers.
- S4. Critique and find errors in proofs, mathematical arguments, and solutions of problems of others.
- S5. Model natural phenomena and use mathematics effectively in the client disciplines such as engineering, physics, computer science, life sciences, management, and business.
- S6. Use appropriate software such as Graphing Calculator, Maple, Mathematica, Fathom, Geometer’s Sketchpad, and Excel to investigate concepts, ideas, and data.
- S7. Effectively use software such as Power Point, MS Word, and TeX to make lively and powerful oral and written presentations.
- S8. Communicate mathematics clearly and logically to others, both orally and in writing.
- S9. Find and evaluate sources of mathematical information, and integrate new knowledge into their knowledge base.

**Values: We aim to produce individuals**

- V1. Who are self-confident, both personally and mathematically.
- V2. Who behave in a harmonious, helpful, and uplifting way with others, including when working on group projects and when explaining mathematics to others.
- V3. Who exhibit positive attitudes towards personal growth and the daily habits that cultivate personal growth and success in life.
- V4. Who are clear on their personal strengths and career goals.
- V5. Who see mathematics as a normal, natural part of their own intelligence, and as a natural foundation for understanding the orderliness at the core of any phenomenon in nature and society.
- V6. Appreciate the source of all knowledge in the Self.

**ETS Major Field Test in Mathematics**

Students in the Mathematics Track of the Mathematics Major take the Educational Testing Service Major Field Test in Mathematics, usually during the Senior Project in their final year. It is expected that students will score in at least the 50 percentile. Less than that is cause for concern.

**Senior Project and Presentation for Math Major**

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 Science of Consciousness. They report on readings or research they conduct on a topic or problem suggested by the course MATH424 Real Analysis 2 or by the course MATH432 Abstract Algebra 2.

Students 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.

The paper is evaluated by the supervisor of that student’s senior project and by at least one other senior faculty member for significant content, significant unification of mathematical principles from all of their courses, and connection to general principles from Maharishi Science of Consciousness. In addition, they are evaluated for information literacy, writing ability according to criteria for modern mathematical writing, and critical thinking.

**Questionnaire**

At the end of each academic year, all mathematics majors are asked to fill out a questionnaire asking for their degree of satisfaction with what they have accomplished during their degree program so far. For students in this track, topics covered are related to the mission, goals, and outcomes of the Mathematics Track of the Mathematics Major.

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