By the time of graduation, mathematics majors will have acquired the following knowledge and skills.
Graduates of our program should understand:
- The role of axioms and assumptions in the formulation of mathematical definitions and theorems.
- The basic rules of logic. They should also have acquired the ability to follow the logical flow of proofs.
- How to distinguish a coherent mathematical argument from a fallacious one.
- The core concepts of analysis and algebra (for graduates in the mathematical options), or key techniques of applied mathematics and the ability to analyze mathematical models (for graduates in the mathematical sciences option).
Problem-Solving and Modeling Skills
Students should be able to:
- Recognize which real-world problems are subject to mathematical reasoning.
- Make vague ideas precise by representing them in mathematical notation, when appropriate.
- Use a variety of techniques for solving problems expressed in mathematical notation.
Graduates should have the ability to:
- Formulate a mathematical statement precisely.
- Develop and write a coherent proof using proper sentence structure and grammar.
- Present a mathematical argument verbally.
- Understand and explain mathematical arguments derived from a variety of sources including textbooks, research papers, and research presentations.
Reading and Research Skills
Students should have:
- Sufficient experience in mathematical language and foundational material to be able to extend their knowledge through independent reading.
- Exposure to and successful experience in solving mathematical problems presenting substantial intellectual challenge.