Mathematics Major

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 rationale 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

Major Learning Outcomes obtained within the Lower Division Core

1. Perform operations on sets and use basic mathematical logic.
2. Represent and solve both theoretical and applied problems using such techniques as graph theory, matrices, sequences, linear programming, difference equations, and combinatorics.

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

1. Set up and solve systems of linear equations using various methods.
2. Work with Vector Spaces and Linear Transformations.
3. Apply matrix techniques to applied problems from various disciplines.

1. Use a variety of algebraic representations to model problem situations.
2. Explain the theory of and operations with groups, rings and fields.
3. Work with advanced algebraic structures and explain how these manifest themselves within the algebra studied in introductory and pre-college mathematics courses.

1. Explain the underlying set, operations, and fundamental axioms that yield the structure of the real number system.
2. Apply analytic techniques to real-world problems.
3. Give a rigorous mathematical explanation of the development of calculus from first axioms.

1. Place mathematical problems in context and explore their relationship with other problems.
2. Solve problems using multiple methods and analyze and evaluate the efficiency of the different methods.
3. Generalize solutions where appropriate and justify conclusions.
4. Use appropriate technologies to conduct investigations, make conjectures, and solve problems.
   

MLO # 11 Mathematics as Communication

Students demonstrate the ability to:

1. Articulate mathematical ideas verbally and in writing, using appropriate terminology.
2. Present mathematical explanations suitable to a variety of audiences with differing levels of mathematical knowledge.
3. Analyze and evaluate the mathematical thinking and strategies of others.
4. Use clarifying and extending questions to learn and to communicate mathematical ideas.
5. Use models, charts, graphs, tables, figures, equations, and appropriate technologies to present mathematical ideas and concepts.

1. Reason both deductively and inductively.
2. Formulate and test conjectures, construct counter-examples, make valid arguments, and judge the validity of mathematical arguments.
3. Present informal and formal proofs in oral and written formats.

MLO # 13 Mathematical Connections

Students demonstrate the ability to:

1. Investigate ways mathematical topics are inter-related.
2. Apply mathematical thinking and modeling to solve problems that arise in other disciplines.
3. Illustrate (when possible), abstract mathematical concepts using applications.
4. Recognize how a given mathematical model can represent a variety of situations.
5. Create a variety of models to represent a single situation.
6. Understand the interconnectedness of topics in mathematics from a historical perspective.

MLO # 14 Technology

Students demonstrate the ability to:

1. Analyze, compare and evaluate the appropriateness of technological tools and their uses in mathematics.
2. 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.
3. To model problem situations and solutions and develop algorithms (including computer programming).

Assessment Pathway for Essential Outcomes (MLO #10 –MLO #14)

Completion of Math 400 and Math 401 with a C or better.

Formative assessment of MLO #10-14 will be built into coursework within the following courses through a variety of approaches, such as student performances, presentations, projects, portfolios, observations and interviews, as well as oral and written examinations.

Formative Assessment is provided in the following courses:

Math 320 Statistics and Probability

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

Math 410 and 411 Modern Algebra I and II

Math 420 and 421 Mathematical Analysis I and II

Summative Assessment is given in the following courses:

Math 400 Capstone Seminar I

Math 401 Capstone Seminar II

Faculty Advisors

Dr. Hongde Hu
Bldg 53 S207 582-3851
hongde_hu@csumb.edu

Dr. Heath Proskin
Bldg 53 S113 582-3219
heath_proskin@csumb.edu

Dr. Michael B. Scott
Bldg 53 S112 582-4229
michael_b_scott@csumb.edu

Dr. Don Pierce
Bldg 53 S208 582-3713
don_pierce@csumb.edu

Dr. Joanne Lieberman
Bldg 53 S209 582-3122
joanne_liebermann@csumb.edu