Credits Required

Credits in the major: 67

Outcomes, Courses and Assessment

Although you officially begin the major when you enroll in MATH 300: Major Proseminar, we encourage you to contact a mathematics faculty advisor as soon as possible. In the Major ProSeminar you will work with the instructor to create your Individual Learning Plan. This ILP maps out how you will achieve each of the Major Learning Outcomes designated below. Your degree culminates in a publicly presented project that displays your cumulative learning in the major. [Learn more at CSUMB.EDU/capstone].

The structure of the major is perhaps most easily understood by grouping the Major Learning Outcomes into four areas. Lower Division Core, Upper Division Core, Area of Concentration, and Essential. A brief description is provided for each of the program Major Learning Outcomes (MLO) directly following the statement of the MLO.

 

Coursework Associated with the Typical Assessment Pathway

Lower Division Core ~ 20 credits

MATH 150: Calculus I   ~ 4 credits  MATH 151: Calculus II  ~ 4 credits  MATH 170: Discrete Mathematics  ~ 4 credits MATH 250: Multivariate Calculus   ~ 4 credits CST 231/L: Problm-Solving/Programng   ~ 4 credits

Upper Division Core ~ 35 credits

MATH 300: Major Proseminar  ~ 4 credits
 
MATH 320: Probability and Statistics  ~ 4 credits MATH 322: Foundations of Modern Math  ~ 4 credits
MATH 330: Linear Algebra  ~ 4 credits MATH 361S: Mathematics Tutors (Service Learning) ~ 5 credits MATH 400: Capstone Seminar  ~ 2 credits
 
MATH 401: Capstone Seminar II  ~ 4 credits

MATH 410: Modern Algebra I  ~ 4 credits MATH 420: Mathematical Analysis I  ~ 4 credits

Concentration ~ 12 credits

Completion of one of the concentrations listed below

Secondary Teaching Concentration

MATH 325: Number Theory ~ 4 credits 
MATH 326: History of Mathematics ~ 4 credits 
MATH 329: College Geometry ~ 4 credits

Pure Math Concentration

MATH 411: Modern Algebra II ~ 4 credits 
MATH 421: Mathematical Analysis II ~ 4 credits 
MATH 340: Differential Equations ~ 4 credits Or MATH 370: Logic and Computation ~ 4 credits

 

Note on MLO 11 - 15

MLOs 10-15 cover knowledge and skills common to all mathematics content areas. These outcomes are central to student success. Because they take time to develop, you receive formative assessment on each within these upper-division mathematics courses:  MATH 320: Probability and Statistics;  MATH 322: Foundations of Modern Math;  MATH 325: Number Theory;  MATH 326: History of Mathematics; MATH 329: College Geometry;  MATH 330: Linear Algebra;  MATH 340: Differential Equations;  MATH 370: Logic and Computation

You can complete your assessment for these MLOs by earning a C or better in the Capstone sequence of  MATH 400: Capstone Seminar and  MATH 401: Capstone Seminar II, or by demonstrating mastery in these 400-level courses: MATH 410: Modern Algebra I; MATH 411: Modern Algebra II; MATH 420: Mathematical Analysis I;  MATH 421: Mathematical Analysis II;  MATH 400: Capstone Seminar;  MATH 401: Capstone Seminar II

The assessment process includes a variety of approaches, such as student performances, presentations, projects, portfolios, observations and interviews, as well as oral and written examinations.

Major Learning Outcomes

MLO 1 Foundations and Calculus

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.

Required Courses

MLO 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.

Required Courses

  • MATH 170: Discrete Mathematics (4 units)

MLO 3 Computer Programming

Students design, develop and document computer programs to solve problems.

Required Courses

  • CST 231: Problm-Solving/Programng (2 units)
  • CST 231L: Prob Solving & Programming Lab (2 units)

MLO 4 Foundation 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.

Required Courses

  • MATH 322: Foundations of Modern Math (4 units)

MLO 5 Statistics and Probability

Students design statistical experiments in which they collect, interpret, present and justify their findings. Students explain and use the idea of density function and associated probabilities of both discrete and continuous probability distributions. Students apply statistical tests, present data and draw inferences from charts, tables and graphs that represent real-world situations.

Required Courses

  • MATH 320: Probability and Statistics (4 units)

MLO 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.

Required Courses

MLO 7 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.

Required Courses

MLO 8 Analysis

 Students explain the underlying set, operations and fundamental axioms that yield the structure of the real number system. Students apply analytic techniques to real-world problems. Students give a rigorous mathematical explanation of the development of calculus from first axioms.

Required Courses

  • MATH 420: Mathematical Analysis I (4 units)

MLO 9 Service Learning

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

  • MATH 361S: Mathematics Tutors (5 units)
  • Or another approved service learning course (see advisor)

MLO 10 Area of Concentration Competency

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

Required Courses

MLO 11 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.

MLO 12 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.

 

MLO 13 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.

MLO 14 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.

MLO 15 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).

Concentrations

Pure Mathematics

Teaching