Mathematics Program

Mathematics encompasses concepts and techniques for exploring and communicating quantitative and spatial relationships. The Heritage University Mathematics program emphasizes applied mathematics for educators and persons in the physical and social sciences. Blending traditional and technology-based skills, students explore concepts numerically, symbolically, algorithmically, and graphically.

Mathematics Program Outcomes

BA Mathematics (5-12) Outcomes
(Adapted from the NCATE Program Standards for Secondary Mathematics Teachers)

Process Standards (Standards 1-7)
Goal 1: Knowledge of Mathematical Problem Solving
Candidates know, understand and apply the process of mathematical problem solving
Goal 2: Knowledge of Reasoning and Proof
Candidates reason, construct and evaluate mathematical arguments and develop an appreciation for mathematical rigor and inquiry.
Goal 3: Knowledge of Mathematical Communication
Candidates communicate their mathematical thinking orally and in writing to peers, faculty and others.
Goal 4: Knowledge of Mathematical Connections
Candidates recognize, use and make connections between and among mathematical ideas and in contexts outside mathematics to build mathematical understanding.
Goal 5: Knowledge of Mathematical Representation
Candidates use varied representations of mathematical ideas to support and deepen their own mathematical understanding.
Goal 6: Knowledge of Technology
Candidates embrace technology as an essential tool for teaching and learning mathematics.
Goal 7: Dispositions
Candidates support a positive disposition toward mathematical processes and mathematical learning. Pedagogy (Standard 8)
Goal 8: Knowledge of Mathematics Pedagogy
Candidates possess a deep understanding of how students learn mathematics and of the pedagogical knowledge specific to mathematics teaching and learning. Content (Standards 9-15)
Goal 9: Knowledge of Number and Operation
Candidates demonstrate computational proficiency, including a conceptual understanding of numbers, ways of representing numbers, relationships among numbers and number systems and meanings of operations.
Goal 10: Knowledge of Different Perspectives on Algebra
Candidates emphasize relationships among quantities, including functions, ways of representing mathematical relationships and the analysis of change.
Goal 11: Knowledge of Geometries
Candidates use spatial visualization and geometric modeling to explore and analyze geometric shapes, structures, and their properties.
Goal 12: Knowledge of Calculus
Candidates demonstrate a conceptual understanding of limits, continuity, differentiation and integration, as well as a thorough background in the techniques and applications of calculus.
Goal 13: Knowledge of Discrete Mathematics
Candidates apply the fundamental ideas of discrete mathematics in the formulation and solution of problems.
Goal 14: Knowledge of Data Analysis, Statistics, and Probability
Candidates demonstrate an understanding of concepts and practices related to data analysis, statistics and probability.
Goal 15: Knowledge of Measurement
Candidates apply and use measurement concepts and tools.

Field-Based Experiences (Standard 16)
Goal 16: Field-Based Experiences
Candidates complete field-based experiences in mathematics classrooms.

B.A. Mathematics, B.A. Interdisciplinary Studies, B.S. Combined Science Outcomes
(Adapted from the MAA CUPM Curriculum Guide)

1. Students will develop mathematical thinking and communication skills.

   1.1 Students will progress from a procedural and computational understanding of mathematics to an understanding that includes logical reasoning, generalization abstraction, and formal proof.

   1.2 Students will solve problems using a variety of approaches, demonstrate persistence in solving complex problems, assess the validity of solutions, pose questions, and devise and test conjectures.

   1.3 Students will carefully analyze data and interpret results intelligently.

   1.4 Students will read mathematics with understanding and communicate mathematical ideas with clarity and coherence through writing and speaking.

2. Students will develop skill with a variety of technological tools.

   2.1 Students will effectively use computer algebra systems, visualization software, statistical packages and computer programming languages.

3. Students will have a broad view of the mathematical sciences and will study particular content areas in depth.

   3.1 Students will solve problems that involve contrasting yet complementary points of view (continuous and discrete, algebraic and geometric, deterministic and stochastic, theoretical and applied) and describe the relationships between these points of view.

   3.2 Students will apply mathematics to solve problems in other disciplines.

   3.3 Students will successfully complete at least two yearlong sequences at the upper-division level and conduct meaningful research projects related to these sequences.

What jobs are available for Mathematics graduates?

• Mathematics teacher
• Researcher
• Actuarial scientist
• Operations researcher
• Financial professional
• Statistician
• Mathematical modeler

Computer Science Program

The Computer Science program encompasses the theory and techniques by which information is encoded, stored, communicated, transformed and analyzed. It deals particularly with the theory of algorithms (i.e., effective procedures), with the structure of languages for expression of algorithms and with the design of efficient algorithms for the solution of practical problems. Of central concern is the study of computer systems (hardware and programs) for the automatic execution of these algorithms.

Computer science has its principle basis in engineering and mathematics. In addition, it draws upon concepts from a wide variety of other disciplines, including linguistics, psychology, biology, philosophy, economics and business. It has applications to these and other disciplines.

B.S. in Computer Science Outcomes
Goal 1: Students will demonstrate subject-matter knowledge in the major.
1.1 Students will have the ability to apply knowledge of computing and mathematics appropriate to their discipline.
1.2 Students will have the ability to understand the fundamental principles of the science of computation, including those of algorithm analysis, software design, operating systems and databases.
1.3 Students will have the ability to analyze a problem and identify and define the computing requirements appropriate to the solution (using efficient algorithms, data structures, etc.).
1.4 Students will have the ability to design, implement, test, and evaluate a computing system, software component, or algorithm to meet required needs and imposed constraints.
1.5 Students will be proficient in the use of more than one programming language.

Goal 2: Students will be prepared to function professionally in the field of computer science.
2.1 Students will demonstrate an understanding of professional and ethical responsibility.
2.2 Students will recognize the responsibilities, ethical, legal, security and social issues in the design and application of computer systems.

Goal 3: Students will be proficient at communicating.
3.1 Students will communicate effectively orally and in writing.
3.2 Students will be able to analyze the local and global impacts of computing on individuals, organizations and society.
3.3 Students will function effectively on teams to accomplish a common goal.

Goal 4: Students will use technology competently.
4.1 Students will have knowledge of contemporary problems and technologies related to computer science.
4.2 Students will be able to use modern software development tools and languages necessary for professional practice.
4.3 Students will recognize the need for and will engage in lifelong learning.

Goal 5: Students will adhere to high standards of professional ethics.
5.1 Students will realize the need for continuing professional development.
5.2 Students will demonstrate a commitment to computer science and its advancement.

What jobs are available for computer science graduates?

• Computer programmer
• System analyst
• Web administrator
• Network administrator
• Security specialist
• Database administrator
• Software engineer

Programs

• Interdisciplinary Studies in Mathematics, A.A.
• Pre-Engineering, A.A.

• Information Technology, B.A.
• Mathematics Education (5-12 Credential), B.A.
• Mathematics, B.A.

• Computer Science, B.S.

Courses

• MATH 436 - Advanced Euclidean Geometry
• MATH 454 - Transformational Geometry
• MATH 462 - Introduction to Real Analysis
• MATH 469 - High School Math from an Advanced Perspective I
• MATH 479 - High School Math from an Advanced Perspective II
• MATH 482 - Introduction to Topology
• MATH 490 - Internship
• MATH 495W - Special Project
• MATH 497W - Senior Thesis