- Students will develop an in-depth integrated knowledge in algebra, geometry, and analysis.
- Students will be able to communicate mathematical ideas and present mathematical arguments both in writing and orally using proper use of mathematical notation and terminology.
- Students will be able to distinguish coherent mathematical arguments from fallacious ones, and to construct complete formal arguments of previously seen or closely-related results.
- Students will be able to give complete solutions to previously seen or closely-related problems.
- Students will be able to use definitions, theorems, and techniques learned to solve problems they haven’t seen before.
- Students will be able to synthesize material from multiple perspectives and make connections with other areas.
- Students will be able to use technology appropriate to each topic.

- Students will learn that mathematics is a discipline of important ideas and that it is essential for students to understand the concepts instead of simply learning to imitate a collection of techniques.
- Students will develop a working knowledge of the particular introductory mathematics course they are taking.
- Students will be able to communicate mathematical ideas in writing and will learn that oral communication in mathematics is important for everyone.
- Students will be able to transfer knowledge of concepts to a variety of practical applications. That is, given a problem they will be able to apply the appropriate mathematical model and technique.
- Students will learn the necessity of justifying mathematical results, as done formally by the instructor by proof or informally by the student with a good and complete argument.
- Students will be able to use technology appropriate to each topic.

**Goal I: Computational Thinking and Problem Solving:** Students will develop problem-solving and critical thinking skills and use these skills to solve complex computing problems.

**Student Learning Outcomes**

Students will:

a) decompose a problem, system or task into parts that are easier to conceive, understand, implement, and maintain

b) recognize patterns among similarities or common differences between a variety of problems

c) use pattern abstraction and generalization in order to manage complexity

d) use stepwise refinement to produce an algorithmic solution to a problem as a result of problem decomposition and pattern identification

**Goal II: Theoretical Foundations:** Students will acquire a working knowledge of the theoretical foundations of computer science.

**Student Learning Outcomes**

Students will:

a) apply mathematical foundations to the discipline of computer science

b) understand the theoretical and practical significance of computational theory and its application to important real-world problem domains

c) use, implement and compare fundamental abstract data types

d) analyze the complexity and computability of algorithmic solutions

e) determine the correctness and efficiency of the design of a software system

**Goal III: Software Engineering Foundation:** Students will acquire both a working knowledge and a theoretical understanding of the professional practice and formal methodologies of development of large software projects.

**Student Learning Objectives**

Students will:

a) understand strategies for effective design and their application in designing computing systems

b) learn to acquire problem requirements and specifications from the client and express them

c) develop and test software solutions using different design methodologies, application program interfaces, and programming languages

d) demonstrate appropriate uses of modern tools of the computing profession

**Goal IV: Communication and Interpersonal Skills:** Students will acquire communication and interpersonal skills necessary to perform effectively in a technical environment.

**Student Learning Outcomes**

Students will:

a) use oral and written communication skills to convey technical information effectively and accurately

b) employ interpersonal skills to work cooperatively and productively in a team environment.

c)communicate effectively with those outside of computing

**Master of Science in Mathematics**

- Students will develop an in-depth integrated knowledge in Algebra and Analysis as well as multiple elective areas of mathematics, beyond the undergraduate level. They will analyze foundational theorems in much greater depth and, exceeding what is expected of an undergraduate mathematics major, give complete proofs of these advanced theorems.
- Students will be able to communicate mathematical ideas and present mathematical arguments both in writing and orally using proper use of mathematical notation and terminology at an advanced level that represents formal mathematical practice.
- Students will be able to give complete solutions to challenging graduate-level mathematical problems.
- Students will be able to synthesize material from multiple perspectives and make connections with other areas of mathematics.
- Students will demonstrate their ability to attain the previous goals during the culminating program oral comprehensive exam and masters essay.

**Master of Arts in Mathematics for High School Teachers**

- Students will develop an in-depth integrated knowledge of topics related to the high school mathematics curriculum.
- Students will be able to gain advanced competence in communicating mathematical ideas and presenting mathematical arguments both in writing and orally using proper use of mathematical notation and terminology.
- Students will master mathematical concepts that they will be able to use to enrich their high school curriculum.
- Students will be able to distinguish coherent mathematical arguments from fallacious ones and to construct precise arguments of previously seen or related results with the goal of teaching their students the importance of giving complete explanations of mathematical ideas.
- Students will be able to synthesize material from multiple perspectives and make connections with other areas of mathematics.
- Students will be able to use mathematics teaching technology appropriate to each mathematical topic.
- Students will demonstrate their ability to attain the previous goals during the culminating program oral comprehensive exam and masters essay.