# B.A./B.S. in Mathematics 2015

The information and requirements given here apply to the 2015–2016 catalog. For other catalog years, please consult the archive.

Upon declaring a major in mathematics, students must select a degree in which the major will appear. We offer your choice of a Bachelor of Arts (B.A.) or Bachelor of Science (B.S.). These degrees have many common requirements, including minimum units, English composition, and many of the general education courses. There are some differences, however.

## Comparing the B.A. and the B.S.

As far as the mathematics coursework is concerned, the B.A. and B.S. are identical: they each require the core courses and one of seven math major options. The requirements for the two degrees differ only in the following ways:

- Second language requirement (details below).
- Science/application course requirements (details below).

## The B.A. in Mathematics

**Language Requirement:**Students must have*fourth semester proficiency*in a second language.- The degree is not science-intensive. Students need to complete only the two Tier One NATS (170) and one Tier Two Natural Science courses, as specified in the University General Education requirements.

## The B.S. in Mathematics

**Language Requirement:**Students must have*second semester proficiency*in a second language.**Laboratory Science Courses Requirement:**The degree is science-intensive and requires one of the following sequences of laboratory science courses:**Application Courses Requirement:**(This requirement does not apply to the Mathematics Education Option.) Students must complete at least six units of non-math coursework with a prerequisite or corequisite of at least Calculus I (MATH 122B or higher). Choose from the following: ABE 201, 284, 428, 481A, 481B; ASTR 250, 302; ATMO 421C, 436A, 469A, 469B; BIOC 462A, 462B, 463A, 466; BME 481B; CE 214; CHEE 201, 201L, 202, 301A, 481A, 481B; CHEM 105A, 105B, 404A, 480A, 480B, 481; CSC 345, 422, 433, 436, 437, 445, 453, 460, 477; CSCV 345; ECE 201R, 381A, 404, 429; ECOL 302, 447, 496N; ECON 332, 361; ENGR 211C, 211P, 265; GEOG 463; GEOS 322, 342, 356, 419, 432, 434A, 440, 469, 479; HWRS 421, 431, 460A; ISTA 352, 421; MCB 303, 305, 480; MSE 345, 404, 415; OPTI 201R, 221, 404; PHYS 131, 140, 141, 142, 143, 151, 152, 161H, 162H, 240, 241, 251, 261H, 440; PSIO 303A, 303B, 304, 472; PTYS 407, 411; SIE 250, 265; SWES 305, 420, 470; WSM 402, 460A; or courses approved by your academic advisor.

**Note:** B.S. students may satisfy both the Laboratory Science Courses Requirement and the Application Courses Requirement by completing one of the Physics sequences. The University's Tier Two General Education Requirement for Natural Science is satisfied for B.S. students by MATH 313, which is one of the Core Courses.

## Double Degrees

Students pursuing a second major that has a degree title different from that of the first major are technically double degree students. Additional requirements may apply to double degree students that do not pertain to double major students (students with two majors that have exactly the same degree title). See an advisor for details.

## Math Major Options

Both the Bachelor of Arts (B.A.) and the Bachelor of Science (B.S.) in Mathematics require a core of basic courses followed by additional courses specific to one of seven possible options:

**Comprehensive Option:**This option prepares students for graduate study in mathematics, applied mathematics, or most other scientific fields.**Computer Science Option:**This option is for students interested in applications of computers to mathematical problems, including math majors who plan to attend graduate school in computer science.**Economics or Business Option:**This option is for students with a particular interest in business applications of mathematics, especially those preparing for graduate school in economics or finance.**General/Applied Mathematics Option:**This option is for students who intend to enter the job market upon graduation, but may also be appropriate for students who plan to go on to graduate school in a field of science or engineering.**Probability and Statistics Option:**This option is for students considering a career as an actuary or statistician, as well as for students wanting to attend graduate school in statistics.**Life Sciences Option:**This option is for students considering a career in medicine, as well as for students wanting to attend graduate school in the biological sciences.**Mathematics Education Option:**This option prepares students for teaching mathematics at the secondary school level. The option has two main components: a set of courses in mathematics, and a set of courses in teaching and learning mathematics in secondary schools.

Each option requires at least 15 units of 400-level mathematics course work, and each option, except Mathematics Education, requires the student to complete a minor. Courses in minors must be distinct from those in the major.

The complete official requirements for each option are given in the *University Catalog* in the form of an *Academic Advisement Report (ADVIP)*. Below we cover the portion of the requirements specific to the mathematics major. It is important for students to consult with their academic advisor about their choice and order of courses, as well as which optional courses would strengthen their degree program.

## Core Courses

The information and requirements given here apply to the 2015–2016 catalog. For other catalog years, please consult the archive.

All seven options for the B.A./B.S. require the following core courses, which should be completed by the end of the sophomore year.

- One of the following two programming courses:
^{(1)} - MATH 122A AND MATH 122B
^{(2)}or MATH 125— Calculus I - MATH 129— Calculus II
- MATH 223— Vector Calculus
- MATH 313— Introduction to Linear Algebra
^{(3)} - MATH 323— Formal Mathematical Reasoning and Writing
^{(4)} - MATH 355— Analysis of Ordinary Differential Equations
^{(5)}

^{(1)} Either CSC 127A or ISTA 130 is recommended for most students. Other courses that can be used to satisfy the programming requirement are: CSC 227, ECE 175, MIS 301, MSE 350, and PHYS 305. These latter courses may require prior programming experience, additional prerequisites and/or a major or minor declared in another subject.

^{(2)} MATH 122A and MATH 122B are a single-semester sequence of courses that cover Calculus I. They are equivalent to the old MATH 124 course, which is no longer offered.

^{(3) }MATH 313 replaces MATH 215 as of fall semester 2015. Students who completed MATH 215 prior to fall 2015 or who have transfer credit equivalent to MATH 215 will still fulfill this requirement, though they will not earn upper-division credit for the course.

^{(4)} MATH 323 is a writing-emphasis course that is the foundation for many of the advanced courses taken by math majors. It should be taken as soon as possible and before most of the 400-level courses in the major. Students who do not do well in MATH 323 should speak to an advisor about their choice of major/option.

^{(5)} MATH 355 is the differential equations course that all mathematics majors are expected to take. This course emphasizes the ideas of dynamical systems and makes use of a more sophisticated approach to differential equations. MATH 254 is a differential equations course that is aimed at preparing students for engineering and science applications. Students with an additional major in engineering or science may ask their math faculty advisors for permission to substitute MATH 254 course for MATH 355 if a scheduling issue arises.

## Comprehensive Option

The information and requirements given here apply to the 2015–2016 catalog. For other catalog years, please consult the archive.

The Academic Program Requirements Report (APRR) gives complete requirements:

This option covers the minimum requirements for admission to most graduate programs in mathematics and applied mathematics. We have separate information on selecting the appropriate option and courses to prepare for various types of graduate programs. Students selecting the comprehensive option should consult with a Mathematics Department faculty advisor in choosing additional course work to ensure that they are prepared for the graduate school of their choice. A minor in any subject is required with this option.

Students completing this option are expected to be proficient in proof writing before beginning most of the 400-level courses below. It is recommended that students who do not earn an A or B in MATH 323 speak with an advisor about their selected math major option before enrolling in proof-intensive 400-level courses.

Major requirements:

- Core Courses
- MATH 413— Linear Algebra
- MATH 424— Theory of Complex Variables
- MATH 425A— Real Analysis of One Variable
- MATH 425B— Real Analysis of Several Variables
- One of the following two pairs: or

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.

## Computer Science Option

The Academic Program Requirements Report (APRR) gives complete requirements:

A minor in computer science is required with this option.

Major requirements:

- Core Courses
- One of the following three sequences: or or
- Two of the following six courses:
- A fifth 400-level course, chosen in consultation with your faculty advisor.

(*) Students minoring in Computer Science may not double-dip courses with their math major, beyond their introductory programming course (i.e. CSC 127A). Students with a double major in Computer Science and Mathematics may be able to double-dip additional courses between the two majors, *within reasonable limits*. It is important to consult with both major advisors when planning your coursework to avoid graduation delays.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.

## Economics or Business Option

The Academic Program Requirements Report (APRR) gives complete requirements:

This option requires either

- an Economics Minor, or
- a Business Administration Minor, or
- a Finance Minor, or
- a Thematic Minor emphasizing courses from two or more disciplines/subject areas such as Economics, Business, and Finance.

The minor should be chosen in consultation with an advisor.

Students completing this option are expected to be proficient in proof writing before beginning their 400-level course work. It is recommended that students who do not earn an A or B in MATH 323 speak with an advisor about their selected math major option before enrolling in 400-level courses.

Major requirements:

- Core Courses
- MATH 425A— Real Analysis of One Variable
- MATH 464— Theory of Probability
- Two of the following four courses:
- A fifth 400-level course, chosen in consultation with your faculty advisor.

For an example of how to order your coursework to heed prerequisites and meet all degree requirements, please consult the sample 4-year plans. You will develop an individualized plan in consultation with your faculty advisor.

## General/Applied Mathematics Option

The Academic Program Requirements Report (APRR) gives complete requirements:

A minor in any subject is required with this option.

Major requirements:

- Core Courses
- MATH 422— Advanced Applied Analysis
- MATH 485— Mathematical Modeling
- One of the following three sequences: or or
- A fifth 400-level course, chosen in consultation with your faculty advisor.

## Probability and Statistics Option

The Academic Program Requirements Report (APRR) gives complete requirements:

A minor in any subject is required with this option. Studies in statistics can equip students for careers working with data in a wide variety of fields, from biology to economics. By discussing with an advisor the choice of the minor, the student can greatly enhance his/her career opportunities. Students who are interested in becoming actuaries will find additional information and suggestions on our Careers in Actuarial Science page.

Students completing this option are expected to be proficient in proof writing before beginning their 400-level course work. It is recommended that students who do not earn an A or B in MATH 323 speak with an advisor about their selected math major option before enrolling in 400-level courses.

Major requirements:

- Core Courses
- MATH 425A— Real Analysis of One Variable
- MATH 464— Theory of Probability
- MATH 466— Theory of Statistics
- One of the following two courses:
- A fifth 400-level course, chosen in consultation with your faculty advisor.

## Life Sciences Option

The Academic Program Requirements Report (APRR) gives complete requirements:

A minor in the biological sciences is required for this option. Possibilities include Astrobiology, Biochemistry, Biology, Biosystems Engineering, Ecology & Evolutionary Biology, Environmental Sciences, Molecular & Cellular Biology, Physiology, Physiological Sciences, and Pre-Health Professions, or a thematic minor with a life sciences emphasis. A second major in a life science area may also be used to fulfill the minor requirement. Courses which may be of interest for your minor include: ECOL 320, 340, 380, 416, 426, 453, 496J; MCB 315, 410, 411, 422.

Major requirements:

- Core Courses
- MATH 422— Advanced Applied Analysis
- MATH 464— Theory of Probability
- MATH 485— Mathematical Modeling
- One of the following two courses:
- One of the following two courses:
- One of the following two courses:

## Mathematics Education Option

The Academic Program Requirements Report (APRR) gives complete requirements:

This option is for students preparing to teach mathematics at the secondary school level. The Education Option has two main components, a set of courses in mathematics, and a set of pedagogy courses. This option does not require a minor. The Math Education Program website contains additional information about admission and requirements.

Major requirements:

- Core Courses
- Courses in Mathematics:
- Courses in Teaching and Learning Mathematics (Pedagogy):
- MATH 205— Teaching Secondary Mathematics
- EDP 301— Educational Psychology and Child and Adolescent Development (replacing STCH 310, which will be discontinued)
- SERP 301B— Inclusive Education for Secondary Students With Diverse Abilities
- The following sequence (required for AZ certification):
- TLS 435— Content Area Literacy in a Multicultural School
- MATH 406A— Curriculum and Assessment in Secondary School Mathematics
- MATH 406B— Methods of Teaching Mathematics in Secondary Schools
- MATH 494C— Student Teaching

- Constitution Requirement for Arizona State certification.
- This requirement is fulfilled by completing one of the following: POL 210 or equivalent; a passing score on the Arizona and US Constitution exams.

- GPA requirements:
- GPA ≥ 2.5 in MATH 122A&B/125, 129, 223, 313
- Pedagogy GPA ≥ 2.5
- Major GPA ≥ 2.0
- Cumulative UA GPA ≥ 2.0