# Learning Goals and Outcomes

### 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.