### MATHEMATICS

**At all levels, Georgetown undergraduates gain knowledge of the following through courses in mathematics:**

- Fundamental objects, techniques and theorems in the mathematical sciences, including the fields of analysis, algebra, geometry, and discrete mathematics;
- The principles of mathematical reasoning and their use in understanding, analyzing and developing formal arguments;
- The connections between the mathematical sciences and other scientific and humanistic disciplines;
- The main forces driving the evolution of the mathematical sciences and their past relevance and future potential for the broader society.

**Through active study of this core body of knowledge, Georgetown mathematics students at all levels develop their ability to:**

- Make significant progress on typical mathematical problems previously unfamiliar to them, using appropriate techniques and tools;
- Formulate precise and relevant conjectures based on examples and counterexamples, prove or disprove conjectures, and translate between intuitive understandings and formal definitions and proofs;
- Construct, modify and analyze mathematical models of systems encountered in disciplines such as physics, economics or biology, assess the models' accuracy and usefulness, and draw contextual conclusions from them;
- Clearly communicate mathematical ideas in appropriate contexts both orally and in writing to a range of audiences, including the educated general public.

### STATISTICS

**At all levels, Georgetown undergraduates gain knowledge of the following through courses in statistics:**

- Fundamentals of probability models and theory underlying statistical methods;
- Principles of statistical reasoning and their use in understanding, analyzing, and developing formal arguments;
- The overall process and particular steps in designing studies, collecting and analyzing data, interpreting and presenting results;
- The role of statistics and its applications in other disciplines, e.g. biological sciences, social sciences, and economics.

**Through the statistics courses they take, Georgetown students at all levels will develop their ability to:**

- Choose appropriate statistical methods and apply them in various data analysis problems;
- Use various statistical software to perform data analysis;
- Communicate effectively statistical methods and results in appropriate contexts, both orally and in writing;
- Critically assess the strengths and weaknesses of published studies, and evaluate the validity of reported results.