B.A./B.S. in Mathematics 2007

The information and requirements given here apply to the 2007 catalog. For other catalogs, please consult the archive.

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 or applied mathematics.
• 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 Finance 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 components: a set of courses in mathematics, and a set of courses in teaching and learning mathematics in secondary schools.

Each option involves at least 15 units of 400-level mathematics courses, 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 official requirements for each option are given in the University Catalog in the form of an Academic Program Requirements Report (APRR). Below we explain the requirements specific to the mathematics major, with links to the APRR for complete requirements. 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.

The B.A. and B.S. in Mathematics differ in the following ways:

• Second Language Proficiency: The B.A. requires 4th semester proficiency, whereas the B.S. requires only 2nd semester proficiency.
• Natural Science Requirement: The B.A. requires two Tier One NATS courses and one Tier Two NATS course, whereas the B.S. requires one of the following sequences of laboratory science courses: PHYS131& 181& 132& 182, PHYS 141& 142, PHYS 141& 241, PHYS 151& 152, PHYS 161H& 162H, CHEM103A& 104A& 103B& 104B, CHEM 105A& 106A& 105B& 106B, MCB 181R& 181L& ECOL 182, GEOS251& 302, GEOS 251& 304, GEOS 302& 304.
• Application Courses Requirement: This requirements applies only to the B.S. (but not 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 124 or higher). Choose from the following: CHEM 105A, 105B, 407, 480A; C SC 345, 346, 422, 433, 436, 437, 445, 453, 460, 473; ECON 332, 361, 411, 421; GEOS 322, 356, 411, 419, 431, 432, 434A, 448; PHYS 131, 132, 141, 142,151, 152, 161H, 162H, 204, 241, 242, 251, 252; or courses approved by your academic advisor.

Note for the B.S.: A student may satisfy the Natural Science 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 by MATH 215, which is part of the Core Courses (see below).

Core Courses

All six options require the following core courses, which should be completed by the end of the sophomore year.

• C SC 127A— Computer Science Principles
• MATH 124or MATH 125— Calculus I
• MATH 129— Calculus II (*)
• MATH 215— Introduction to Linear Algebra
• MATH 223— Vector Calculus
• MATH 323— Formal Mathematical Reasoning and Writing (†)
• MATH 355— Analysis of Ordinary Differential Equations (*)

(*) The pair MATH 129 and MATH 355 may be replaced with MATH 250Aand MATH 250B(Calculus and Differential Equations I and II).

(†) MATH 323 is a writing-emphasis course that is the foundation for the advanced courses taken by any math major. It should be taken as soon as possible and before most of the 400-level courses in the major. Students who do not earn at least a C in MATH 323 should reconsider their choice of major.

Comprehensive Option

This option covers the minimum requirements for admission to most graduate programs in mathematics and applied mathematics. Students selecting this option should consult with a Mathematics Department 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.

Major requirements:

• Core Courses (see above)
• MATH 413— Linear Algebra
• MATH 424— Elements of Complex Variables
• MATH 425A— Real Analysis of One Variable
• MATH 425B— Real Analysis of Several Variables
• One of the following two pairs:
  1. MATH 415A— Introduction to Abstract Algebra
  2. MATH 415B— Second Course in Abstract Algebra
  or
  1. MATH 454— Ordinary Differential Equations and Stability Theory
  2. MATH 456— Applied Partial Differential Equations

Computer Science Option

A minor in computer science is required with this option.

Major requirements:

• Core Courses (see above)
• One of the following three sequences:
  1. MATH 415A— Introduction to Abstract Algebra
  2. MATH 415B— Second Course in Abstract Algebra
  or
  1. MATH 464— Theory of Probability
  2. MATH 466— Theory of Statistics
  or
  1. MATH 475A— Mathematical Principles of Numerical Analysis
  2. MATH 475B— Mathematical Principles of Numerical Analysis
• Two of the following six courses:
  • MATH 413— Linear Algebra
  • MATH 443— Theory of Graphs and Networks
  • MATH 445— Introduction to Cryptography
  • MATH 446— Theory of Numbers
  • MATH 447— Combinatorial Mathematics
  • MATH 479— Game Theory and Mathematical Programming
• A fifth 400-level course, chosen in consultation with your faculty advisor.

Economics or Finance Option

This option requires either a minor in economics or a thematic minor emphasizing courses in finance. The minor should be chosen in consultation with an advisor.

Major requirements:

• Core Courses (see above)
• MATH 425A — Real Analysis of One Variable
• MATH 464 — Theory of Probability
• One of the following two courses:
  • MATH 410— Matrix Analysis
  • MATH 413— Linear Algebra
• One of the following three courses:
  • MATH 425B— Real Analysis of Several Variables
  • MATH 466— Theory of Statistics
  • MATH 468— Applied Stochastic Processes
• A fifth 400-level course, chosen in consultation with your faculty advisor.

General/Applied Mathematics Option

A minor in any subject is required with this option.

Major requirements:

• Core Courses (see above)
• MATH 422— Advanced Applied Analysis
• MATH 485— Mathematical Modeling
• One of the following three sequences:
  1. MATH 454— Intermediate Ordinary Differential Equations
  2. MATH 456— Applied Partial Differential Equations
  or
  1. MATH 464— Theory of Probability
  2. MATH 466— Theory of Statistics
  or
  1. MATH 475A— Mathematical Principles of Numerical Analysis
  2. MATH 475B— Mathematical Principles of Numerical Analysis
• A fifth 400-level course, chosen in consultation with your faculty advisor.

Probability and Statistics Option

A minor is required with this option. By discussing with an advisor the choice of the minor, the student can greatly enhance his/her career opportunities. For additional information and suggestions, see the Probability and Statistics Webpage maintained by Professor Donald Myers.

Major requirements:

• Core Courses (see above)
• MATH 425A— Real Analysis of One Variable
• MATH 464— Theory of Probability
• MATH 466— Theory of Statistics
• One of the following two courses:
  • MATH 468— Applied Stochastic Processes
  • MATH 413— Linear Algebra
• A fifth 400-level course, chosen in consultation with your faculty advisor.

Life Sciences Option

A minor in the biological sciences is required for this option. Possibilities include BIOC, GBIO, ECOL, MCB, MICR, PS, PSIO, V SC, and PL S, or a thematic minor with a life sciences emphasis. Courses which may be of interest for your minor include: ECOL 320, 340, 380, 380L, 416, 426, 429, 453, 496J, 496Y; MCB 410,411, 422, 471A.

Major requirements:

• Core Courses (see above)
• MATH 422— Advanced Applied Analysis
• MATH 464— Theory of Probability
• One of the following three courses:
  • MATH 380— Math Models in Biology
  • MATH 485— Mathematical Modeling
  • MATH 496N— Non-Linear Dynamics of Biological Systems
• One of the following two courses:
  • MATH 410— Matrix Analysis
  • MATH 413— Linear Algebra
• One of the following two courses:
  • MATH 454— Ordinary Differential Equations and Stability Theory
  • MATH 456— Applied Partial Differential Equations
• One of the following two courses:
  • MATH 466— Theory of Statistics
  • MATH 468— Applied Stochastic Processes

Mathematics Education Option

This option is for students preparing to teach mathematics at the secondary school level. The Education Option has two components, a set of courses in mathematics, and a set of courses in teaching and learning mathematics in secondary schools. This option does not require a minor.

Major requirements:

• Core Courses (see above)
• Courses in Mathematics:
  • MATH 315— Introduction to Number Theory and Modern Algebra
  • MATH 330— Topics in Geometry
  • MATH 362— Introduction to Probability Theory
  • MATH 404— History of Mathematics
  • MATH 407— Synthesis of Mathematical Concepts
• Courses in Teaching and Learning Mathematics:
  • STCH 250— Teaching Mathematics
  • STCH 310— Adolescent Development and Learning
  • LRC 416— Intro to Structured English Immersion
  • LRC 435— Literacy/Diversity
  • SERP 301B— Mainstreaming
  • MATH 406A— Curriculum and Assessment in Mathematics
  • MATH 406B— Methods of Teaching Mathematics in Secondary School
  • STCH 494C— Student Teaching

Additional certification requirement: Successful completion of coursework or examinations in U.S. and Arizona Constitutions is required for certification. Consult with your advisor.