Total credits: 124
Credits in the major: 60
Although you officially begin the major when you enroll in the 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].
MATH 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.
MATH 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.
MATH MLO 3 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.
MATH MLO 4 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.
MATH MLO 5 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.
MATH MLO 6 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.
MATH MLO 7 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.
MATH MLO 8 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.
MATH MLO 9 Area of Concentration Competency ~ Students demonstrate depth in a chosen area of mathematics by completing an appropriate sequence of learning experiences.
Assessment for Pure Mathematics Concentration
Assessment for Secondary Teaching Concentration
MATH MLO 10 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.
MATH MLO 11 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.
MATH MLO 12 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.
MATH MLO 13 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.
MATH MLO 14 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).
Assessment for Essential Learning Outcomes
MLOs 9-14 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 Statistics and Probability; MATH 325 Number Theory; MATH 326 History 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 and MATH 401, or by demonstrating mastery in these 400-level courses: MATH 411 Modern Algebra II; MATH 420 Mathematical Analysis I; MATH 421 Mathematical Analysis II; MATH 400 Capstone I; MATH 401 Capstone 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.