1. A Tale of Two (or more) Cultures Develop understanding and appreciation of the distinct environments at major mathematics departments and at undergraduate institutions with significant concentrations of students from groups underrepresented in mathematics Articulate priorities for aspects of undergraduate mathematics preparation that provide the greatest foundation for success in graduate study Consider strategies, near- and long-term, for graduate departments looking to diversify, with a particular eye on bridges to success for students who have adequate- -but not ideal--undergraduate preparation for a given doctoral program

2. Ideal Preparation? Excellent performance in undergraduate mathematics coursework, demonstrated by grades of mostly A's, especially in certain core courses like analysis Engagement in undergraduate mathematics research Participation in summer enrichment programs Participation in mathematics competitions, like the Putnam

3. Ideal Preparation, cont. Strong in computer programming and/or use of mathematical software platforms like Mathematica High GRE scores on the Mathematics subject test Confidence in mathematical ability Ability to work independently Ability to work collaboratively Broad course preparation and exposure Deep course preparation and understanding

4. Other Considerations Issues of pedagogy in mathematics classes-- lectures, workshops, labs, development of mathematical community Development of abilities to comprehend and construct proofs when challenged in limited time by desire to develop proficiency with modern mathematics technology Preparation for graduate work in mathematics versus “applied mathematics” versus statistics graduate programs—any distinctions?