Program Learning Outcomes

Upon completion of the programs, students will be able to:

B.S. in Mathematics

1. Demonstrate mastery of basic mathematical ideas and techniques, ranging across the following fields – single and multivariate calculus, linear algebra, real analysis, probability/statistics, basic differential equations, and mathematical modeling.
2. Demonstrate an understanding of the nature of proof.
3. Demonstrate the ability to think analytically and critically and to formulate problems, solve them, and interpret their solutions, both collaboratively and individually.
4. Demonstrate the ability to use technological tools (e.g., algebraic and visualization software, statistical packages, a high-level programming language).
5. Demonstrate the ability to apply knowledge from one branch of mathematics to another and from mathematics to other disciplines.
6. Demonstrate the ability to communicate mathematics both orally and in writing.
7. Demonstrate an understanding of the foundational ideas in abstract algebra, including groups, rings, and fields.
8. Demonstrate an understanding of foundational ideas in real analysis.

B.S. in Mathematics, Option in Applied Math

1. Demonstrate mastery of basic mathematical ideas and techniques, ranging across the following fields – single and multivariate calculus, linear algebra, real analysis, probability/statistics, basic differential equations, and mathematical modeling.
2. Demonstrate an understanding of the nature of proof.
3. Demonstrate the ability to think analytically and critically and to formulate problems, solve them, and interpret their solutions, both collaboratively and individually.
4. Demonstrate the ability to use technological tools (e.g., algebraic and visualization software, statistical packages, a high-level programming language).
5. Demonstrate the ability to apply knowledge from one branch of mathematics to another and from mathematics to other disciplines.
6. Demonstrate the ability to communicate mathematics both orally and in writing.
7. Demonstrate an understanding of numerical analysis, differential equations, and computer programming.
8. Demonstrate the ability to apply their mathematical knowledge to model and solve real world problems.

B.S. in Mathematics, Option in Math Education

1. Demonstrate mastery of basic mathematical ideas and techniques, ranging across the following fields – single and multivariate calculus, linear algebra, real analysis, probability/statistics, basic differential equations, and mathematical modeling.
2. Demonstrate an understanding of the nature of proof.
3. Demonstrate the ability to think analytically and critically and to formulate problems, solve them, and interpret their solutions, both collaboratively and individually.
4. Demonstrate the ability to use technological tools (e.g., algebraic and visualization software, statistical packages, a high-level programming language).
5. Demonstrate the ability to apply knowledge from one branch of mathematics to another and from mathematics to other disciplines.
6. Demonstrate the ability to communicate mathematics both orally and in writing.
7. Demonstrate mastery of foundational geometric concepts and aspects of the history of mathematics.
8. Demonstrate the ability to bridge understandings of components of their major coursework to issues and content in secondary mathematics.
9. Demonstrate the mathematical processes as articulated in the Standards for Mathematical Practices (CA Common Core State Standards).

B.S. in Applied Statistics

1. Demonstrate mastery of basic mathematical ideas and techniques, ranging across the following fields – single and multivariate calculus, linear algebra, real analysis, probability/statistics, basic differential equations, and mathematical modeling.
2. Demonstrate an understanding of the nature of proof.
3. Demonstrate the ability to think analytically and critically and to formulate problems, solve them, and interpret their solutions, both collaboratively and individually.
4. Demonstrate the ability to use technological tools (e.g., algebraic and visualization software, statistical packages, a high-level programming language).
5. Demonstrate proficiency in communicating complex results to a diverse audience with clarity.
6. Demonstrate a commitment to collecting and managing data responsibly and ethically, and the ability to discern appropriate methods for analyzing various types of data.
7. Demonstrate proficiency in coding and computation for organizing, summarizing, and analyzing raw data collected from a diverse array of contexts, using technology to draw conclusions and make actionable decisions.
8. Demonstrate the ability to think critically and abstractly about the mathematical foundations for statistics and data science, and their application to real data.
9. Demonstrate skill in collaborative problem solving for large scale projects involving data from a wide variety of domains.

M.S. in Mathematics

1. Demonstrate the ability to think analytically and critically and to formulate problems, solve them, and interpret their solutions, both collaboratively and individually.
2. Demonstrate expanded or deepened mathematical content understanding.
3. Demonstrate the ability to communicate mathematics both orally and in writing.
4. Demonstrate the advanced ability to write and read proofs.
5. Demonstrate mastery of advanced abstract algebra and geometry concepts, as well as mastery of advanced analysis and/or topology.

M.S. in Mathematics, Option in Applied Math

1. Demonstrate the ability to think analytically and critically and to formulate problems, solve them, and interpret their solutions, both collaboratively and individually.
2. Demonstrate expanded or deepened mathematical content understanding.
3. Demonstrate the ability to communicate mathematics both orally and in writing.
4. Demonstrate mastery of numerical analysis, ordinary differential equations, and partial differential equations.
5. Demonstrate the ability to apply their mathematical knowledge to model and solve real world problems.
6. Demonstrate the ability to program using current technologies.

M.S. in Mathematics, Option in Math Education

1. Demonstrate the ability to think analytically and critically and to formulate problems, solve them, and interpret their solutions, both collaboratively and individually.
2. Demonstrate expanded/deepened mathematical/statistical content understandings.
3. Demonstrate the ability to communicate mathematics/statistics both orally and in writing.
4. Demonstrate an understanding both orally and in writing of current recommendations at both the state and national levels for mathematics education and how they compare to other countries.
5. Demonstrate an ability to analyze research in mathematics education.
6. Demonstrate an understanding of the historical perspective of mathematics education.
7. Demonstrate an understanding of pedagogical and assessment practices appropriate to facilitate the learning of mathematics for all secondary students, including students engaging in mathematics in ways aligned with the Standards for Mathematical Practices.

M.S. in Applied Statistics

1. Demonstrate the ability to think analytically and critically and to formulate problems, solve them, and interpret their solutions, both collaboratively and individually.
2. Demonstrate expanded or deepened mathematical content understanding.
3. Demonstrate the ability to communicate mathematics both orally and in writing.
4. Demonstrate an understanding of the theoretical foundation of the methods and techniques of statistical inference.
5. Demonstrate a thorough knowledge of design of experiments to permit efficient analysis of sources of variation with application to quality assurance and demonstrate the ability to adapt these methods to the solution of a given real-world problem.
6. Demonstrate a working knowledge of the use of statistical software such as SAS and SPSS in applications of statistics, including the ability to analyze data and interpret program output.