Mathematics Department Goals and ObjectivesStarting with the mathematical concepts of number, shape, and function and the process of formal, logical reasoning, we seek to recognize patterns and relationships and articulate them as mathematical truths. These patterns and relationships are formulated as formally defined mathematical objects or axiomatic systems, which are abstracted from objects or processes that come from the physical or human world (with number and shape as the primary examples) or generalized from other mathematical forms. The truths we then seek are rigorously derived using proof.
The methods of inquiry we use are inductive and deductive. Deductive reasoning comprises the formal side of mathematics, the process by which one moves from axioms and definitions to mathematical truths via formal, logical reasoning. Inductive reasoning comprises the ``informal'' side of mathematics, the process by which one identifies patterns and connections and generalizations, leading to new axioms or definitions or new potential mathematical truths, which are then investigated formally via deductive reasoning.
Critical thinking, formal reasoning, and effective communication of ideas in both written and oral form are central both to the study of mathematics and the liberal arts enterprise * Students should enter the curriculum at an appropriate place and level.
* Students should be able to choose from a broad spectrum of mathematical or statistical offerings that engages their personal intellectual interests, allies with and supports their curricular program of study, and/or satisfies major or college-wide requirements.
* Students should understand mathematics as both an object of study in itself as well as a tool for application.
* Students should be able to apply mathematics or statistics to a range of situations by logically, precisely, and creatively formulating problems, solving them, and interpreting the solutions.
* Students should understand the interplay among applications, problem-solving, and theory.
Math 100 is a pre-calculus course for students who come to Vassar with a very weak mathematical background. The calculus is both a brilliant human achievement as well as the language of many mathematical models in the physical, natural, and social sciences, and Math 101/102 and 121/122/125 allow students to engage in the calculus in a number of different ways appropriate to their particular goals and backgrounds. Additionally, Math 131 covers a wide range of mathematical topics in the form of a Freshman Writing Seminar; Math 141 provides basic statistical thinking and skills. Both of these are at a level appropriate to any Vassar student.
The 200 level features courses that tend to be a mix of theory and application. Math 221, 222, 228, and 263 are required or recommended by other departments. Math 221, 231, 261, and 263 expose students to the more abstract, theoretical side of mathematics.
All of the goals for nonmajors apply to majors and correlates as well. Additionally for both majors and correlates:
* Students should possess a core knowledge of mathematical disciplines, including single variable and vector calculus and linear algebra for both correlates and majors, and additionally analysis and algebra for majors.
* Students should develop an appreciation of different areas of mathematics and their relationship to each other and to other disciplines.
* Students should appreciate the roles of intuition and formality in mathematics.
* Students should be able to work both independently and collaboratively.
* Students should be able to read, absorb, discuss, write, and speak about mathematics.
* Students should and have a broad understanding of logical reasoning, generalization, abstraction, and formal proof.
Additionally, for majors:
* Students should be prepared for a career that uses mathematical skills, for graduate programs in mathematics or fields that use mathematics, or for a teaching career at either the elementary or secondary level.
The required 221/222 sequence presents core material. Math 221 in particular also serves as a serious introduction to abstract, proof-oriented mathematics. Math 231, 261, and 263 support this "transition to higher mathematics" function. Math 321 and 361 present the core analytical and algebraic material and bring student's abilities with abstraction and proof to a mathematically mature level. The remainder of the 300 level supports this maturation process while providing a range of content. The "advanced" 300 level courses (those that have 300 level prerequisites) additionally prepare students for graduate work in terms of content, speed, and pedagogical mode, with most either containing a presentation component or taught completely in seminar style so that students must, either independently or in groups, read and absorb material and then successfully communicate it to their fellow students in class. Math 301, the capstone seminar, is always taught in seminar style using material that synthesizes the student's experience in the major.