Mathematics M.S./Ph.D. Learning Outcomes

PLO 1. Core Knowledge

Students will be able to:

• Demonstrate a general knowledge of mathematics consistent with that of a faculty member at a research university. IN particular, students should be proficient at the graduate level in the core areas of Real Analysis, Complex Analysis and Algebra. 
• Demonstrate specialized knowledge of mathematics sufficient to carry out substantive independent research.

PLO 2. Research Methods and Analysis

Students should be able to:

• Understand the range of tools appropriate for research in their mathematics sub-field. This can range from theoretical analysis techniques in pure mathematics to modeling and numerical simulation in applied mathematics. 
• Read, synthesize and critically evaluate research in their subfield of mathematics. 
• Understand how their research tools, and results, fit in their subfield and understand their significance in a broader context of mathematics or science. 
• Identify, formulate and investigate an independent, advanced research project guided by prior research in theory and applications, in appropriate. 
• Understand and follow research ethics.

PLO 3. Pedagogy

Students will be able to:

• Communicate effectively to large and small groups in pedagogical settings such as discussions formats (and also in lecture formats). 
• Design high-quality undergraduate and graduate courses in mathematics, including appropriate goals, reading or audiovisual materials, assignments, and sequencing.
• Identify and effectively deploy suitable technologies for use in all aspects of instruction. 
• Assess students effectively, including developing and using appropriate measures and rubrics.

PLO 4. Scholarly Communication

Students will be able to:

• Structure a coherent and convincing mathematical argument. 
• Review and cogently discuss relevant literature and their significance. 
• Write in a level and style consistent with that found in leading mathematics journals. 
• Understand and properly use styles of citing, referencing, and formatting found in journals in mathematics and related fields.

PLO 5. Professionalism

Students will be able to:

• Select appropriate conference venues for their mathematics research (as well as application areas) 
• Write compelling abstracts describing their research for consideration at research conferences in mathematics, or appropriate application areas. 
• Prepare talks (both short and long) suitable for presentation at a research conference. 
• Prepare manuscripts that meet the standards of specific mathematics journals and respond appropriately to recommendations for revisions.
• Select appropriate fellowship or grand opportunities and prepare competitive proposals for themselves. 
• Make effective contributions to research teams and learning seminars. 
• Make effective contributions to department, university, community, and professional service. 
• Mentor junior Researchers (e.g., undergraduates, beginning graduate students)

PLO 6. Independent Research

Students should be able to:

• Develop their own research projects that meet high standards of theoretical and methodological rigor with lasting impact.
• Produce scholarship that is comparable in scope and format to articles that appear in leading peer-reviewed journals in mathematics, as well as application areas. 
• Supervise junior researchers (e.g., high school students, undergraduates, beginning graduate students) effectively

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