Mathematics B. S. ~ Program RequirementsCredits in the major: 67Outcomes, Courses and AssessmentAlthough you officially begin the major when you enroll in MATH 300, 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 Upper Division Core ~ 35 credits Math 300 Major ProSeminar ~ 4 credits Concentration ~ 12 credits Completion of one of the concentrations listed belowSecondary Teaching Concentration Math 325 Number Theory ~ 4 creditsMath 326 History of Math ~ 4 credits Math 329 College Geometry ~ 4 credits Pure Math Concentration Math 411 Modern Algebra II ~ 4 creditsMath 421 Mathematical Analysis II ~ 4 credits Math 340 Differential Equations ~ 4 credits Or Math 370 Logic and Computation ~ 4 credits Learning Outcomes ~ Lower-Division CoreMATH 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 Computer Programming ~ Students design, develop and document computer programs to solve problems.
Learning Outcomes ~ Upper-Division CoreMATH 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.
MATH 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.
MATH 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.
MATH 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.
MATH 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.
MATH 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.
Learning Outcomes Obtained Within ConcentrationMATH MLO 10 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
Essential Learning OutcomesMATH 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. MATH 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. MATH 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. MATH 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. MATH 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). Assessment for Essential Learning Outcomes 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; MATH 322; MATH 325; MATH 326; MATH 329; MATH 330; MATH 340; MATH 370 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; MATH 420; MATH 421; MATH 400; MATH 401 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. |