| Learning Goals |
Learning Objectives |
| Students will... |
Students will be able to... |
| Strengthen their problem-solving skills and further develop their mathematical maturity |
- Make use of reasoning along with suitable theorems, ideas, or methods of proof to solve problems and prove mathematical facts
- Correctly implement suitable algorithms and perform multi-step computations
- Interpret and evaluate the practical merits of computed answers |
| Understand, evaluate, and interpret quantitative information given in a variety of formats |
- Make estimates and apply data given in graphical, tabular, or algebraic formats, and translate data between various formats
- Sketch graphs of given formulaic relationships with input from calculus, and identify and interpret graphical representations |
| Understand the need for proof and what comprises mathematical proof |
- Correctly apply techniques of logic and abstract reasoning in formulating and proving statements
- Read, write and understand proofs, and evaluate the correctness of a given proof
- Use various proof techniques successfully |
| Have a working knowledge of foundational technical material |
- Understand and express the statements of key theorems, and identify the main ideas in the proofs of certain of these theorems
- Analyze various mathematical situations and codify them in suitable mathematical language
- Understand and express conceptual motivations for computations |
| Know how to frame appropriate real-world problems in mathematical language |
- Use data in various forms to set up an abstract mathematical version of a problem
- Translate between information in practical real-world scenarios and the mathematical context, and back
- Recognize real-world manifestations of concepts from calculus and other mathematical disciplines, and problems to which these subjects can be applied |
| Skillfully communicate (both orally and in writing) mathematical ideas and applications |
- Explain mathematical processes and computations to others (both mathematicians and a general audience), orally or in writing
- Collaborate with others in the formulation, solution, and presentation of a [calculus, etc.] problem
- Use professional and domain-specific terminology correctly |
| Demonstrate competency in probability and financial mathematics |
- Show solid understanding and apply common distributions (binomial, Poisson, Normal, exponential)
- Work with joint distributions, and identify linear relations between two random variables
- Demonstrate solid understanding of central limit theorem and apply it
- Show solid understanding and apply the theory of interest |