# Learning Goals And Outcomes

#### Undergraduate Program

### 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 modelsâ€™ 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.

#### GRADUATE PROGRAM

### LEARNING GOALS

- Master the subject material in the four required core courses that form the academic pillars of the program: Probability, Applied Mathematics, Statistics, and Numerical Analysis.
- Develop a client-based and practical perspective concerning applied mathematics and statistics at the MS level, with a view towards solving real-world modeling and computational problems that arise in realistic situations.
- Obtain hands-on experience in client-based operations through internships and consulting seminars, thereby developing the ability to collaborate with individuals whose training lies in other disciplines.
- Become sufficiently proficient in the core academic material to permit further study at the PhD level in applied mathematics, statistics, and related areas.

### Learning Outcomes

- Students will be able to compete successfully for internship and employment positions in government, industry, and non-profit organizations.
- Graduates will have a predisposition for outreach toward application areas such as physical sciences, financial services, and social sciences and have the knowledge, experience, and motivation to bring the tools of mathematics and statistics to bear on real-world problems.
- Alumni will have the communication skills necessary to successfully collaborate with non-expert users of applied mathematics and statistics.
- Graduates will have the intellectual curiosity and flexibility to grow with developing technology and new methods in mathematics and statistics.