Major Requirements

Pure Mathematics Requirements

Credits Required: 

Total credits: 120

Credits in the major: 72

If you are interested in majoring in mathematics, you are encouraged to contact a mathematics faculty advisor as soon as possible (see the advising page for more information). You will work with a faculty advisor to create your Individual Learning Plan. This ILP maps out how you will achieve each of the Major Learning Outcomes designated below and earn your degree.

The structure of the major is perhaps most easily understood by grouping the courses into four areas. Lower Division Core (24 credits), Upper Division Core (36 credits), Area of Concentration (12 credits), and General Education Requirements (46 credits). Each course is assessed based on one more of the Major Learning Outcomes for the major. A brief description is provided for each of the program Major Learning Outcomes (MLO) directly following the statement of the MLO.

Note on MLOs 3 - 7

MLOs 3-7 cover knowledge and skills common to all mathematics content areas. These outcomes are central to student success. Because they take time to develop, students receive formative assessment within each mathematics course.  

Students can complete their assessment for these MLOs by earning a C or better in MATH 300: Major Proseminar and MATH 400: Capstone Seminar. Assessment includes a variety of approaches, such as student performances, presentations, projects, portfolios, observations and interviews, as well as oral and written examinations.

Major Requirements and Learning Outcomes are identified below. In order to graduate, students must also meet all general education and university requirements. 

Core Courses

  • Lower Division Core ~ 24 credits
  • MATH 150: Calculus I (4 units)
  • MATH 151: Calculus II (4 units)
  • MATH 170: Discrete Mathematics (4 units)
  • MATH 250: Multivariate Calculus (4 units)
  • MATH 265: Diff Equs & Linear Algebra (4 units)
  • CST 231/L: Problm-Solving/Programng (4 units)
  • Upper Division Core ~ 36 credits
  • MATH 300: Major Proseminar (4 units)
  • MATH 320: Probability and Statistics (4 units)
  • MATH 322: Foundations of Modern Math (4 units)
  • MATH 330: Advanced Linear Algebra (4 units)
  • MATH 350: Complex Analysis (4 units)
  • MATH 400: Capstone Seminar (4 units)
  • MATH 410: Modern Algebra I (4 units)
  • MATH 420: Mathematical Analysis I (4 units)
  • Upper Division Service Learning (One of the following) ~5 credits
  • MATH 361S: Mathematics Tutors (5 units)
  • MATH 362S: Mathematics Consultants (5 units)
  • Pure Mathematics Concentration
  • MATH 411: Modern Algebra II (4 units)
  • MATH 421: Mathematical Analysis II (4 units)
  • AND one of the following Electives:
  • MATH 340: Ordinary Diff Equations (4 units)
  • MATH 370: Logic & Computation (4 units)
  • MATH 374: Mathematical Modeling (4 units)
  • MATH 375: Num Analysis Math & Stat (4 units)
  • MATH 376: Partial Differential Equs (4 units)
  • MATH 385: Enumerative Combinatorics (4 units)
  • MATH 386: Graph Theory and Its Appl (4 units)
  • STAT 250: Applied Stat:Sci Tech (4 units)
  • STAT 320: Mathematical Statistics (4 units)
  • STAT 400: App Stat Meth:Regr Analys (4 units)

MLO 1 Mathematical Content

  1. Calculus and Differential Equations. Students explain and apply the basic concepts of single and multivariate calculus including the various forms of derivatives and integrals, differential equations, their interconnections and their uses in analyzing and solving real-world problems. 
  2. Discrete Mathematics. Students perform operations on sets and use basic mathematical logic. Students represent and solve both theoretical and applied problems using such techniques as graph theory, matrices, sequences, linear programming, difference equations and combinatorics.
  3. Computer Programming. Students design, develop and document computer programs to solve problems.
  4. Foundations of Modern Mathematics. Students explain the nature and purpose of axiomatic systems, utilize various methods of mathematical proof and prove fundamental theorems utilizing various axiomatic systems.
  5. Statistics and Probability. Students use a variety of methods and techniques to determine the probability of an event or events, including the use of density functions and associated probabilities of both discrete and continuous probability distributions. Students work with applications of probability to mathematical statistics such as point estimation and hypothesis testing.
  6. Linear Algebra. Students set up and solve systems of linear equations using various methods. Students work with vector spaces and linear transformations. Students apply matrix techniques to applied problems from various disciplines.
  7. Abstract Algebra. Students use a variety of algebraic representations to model problem situations. Students explain the theory of and operations with groups, rings and fields. Students work with advanced algebraic structures and explain how these manifest themselves within the algebra studied in introductory and pre-college mathematics courses.
  8. Real and Complex Analysis. Students explain the underlying set, operations and fundamental axioms that yield the structure of the real and complex number system. Students apply analytic techniques to real-world problems. Students give a rigorous mathematical explanation of the development of calculus from first axioms.

  9. Area of Concentration Competency. Students demonstrate depth in a chosen area of mathematics by completing an appropriate sequence of learning experiences.

Required Courses

MLO 2 Service to the Community

Students demonstrate the ability to combine disciplinary knowledge and community experiences to share the relevance and importance of mathematics with culturally, linguistically, technologically and economically diverse populations in the context of issues of social responsibility, justice, diversity and compassion.

Required Courses

MLO 3 Problem Solving

Students demonstrate the ability to: (a) place mathematical problems in context and explore their relationship with other problems; (b) solve problems using multiple methods and analyze and evaluate the efficiency of the different methods; (c) generalize solutions where appropriate and justify conclusions; and (d) use appropriate technologies to conduct investigations, make conjectures and solve problems.

Required Courses

MLO 4 Mathematics as Communication

Students demonstrate the ability to: (a) articulate mathematical ideas verbally and in writing, using appropriate terminology; (b) present mathematical explanations suitable to a variety of audiences with differing levels of mathematical knowledge; (c) analyze and evaluate the mathematical thinking and strategies of others; (d) use clarifying and extending questions to learn and communicate mathematical ideas; and (e) use models, charts, graphs, tables, figures, equations and appropriate technologies to present mathematical ideas and concepts.

Required Courses

MLO 5 Mathematical Reasoning

Students demonstrate the ability to: (a) reason both deductively and inductively; (b) formulate and test conjectures, construct counter-examples, make valid arguments and judge the validity of mathematical arguments; and (c) present informal and formal proofs in oral and written formats.

Required Courses

MLO 6 Mathematical Connections

Students demonstrate the ability to: (a) investigate ways mathematical topics are interrelated; (b) apply mathematical thinking and modeling to solve problems that arise in other disciplines; (c) illustrate, when possible, abstract mathematical concepts using applications; (d) recognize how a given mathematical model can represent a variety of situations; (e) create a variety of models to represent a single situation; and (f) understand the interconnectedness of topics in mathematics from a historical perspective.

Required Courses

MLO 7 Technology

Students demonstrate the ability to: (a) analyze, compare and evaluate the appropriateness of technological tools and their uses in mathematics; (b) use technological tools such as computers, calculators, graphing utilities, video and other interactive programs to learn concepts, explore new theories, conduct investigations, make conjectures and solve problems; and (c) model problem situations and solutions, and develop algorithms (including computer programming).

Required Courses

Concentrations

Mathematics Subject Matter Preparation Program

Pure Mathematics