Research Interests

Selected Publications

• M.A. Sorto, Max Warshauer, T. McCabe, H. Warshauer, Understanding the Value of a Question: An Analysis of a Lesson, Journal of Mathematica Sciences and Mathematics Edcation, 4(1): 50 - 60, 2009.
• Max L. Warshauer, E. Curtin; The Locker Puzzle, The Mathematical Intelligencer, Vol. 28, Number 1, 2006.
• Max L. Warshauer, Terry McCabe, Hiroko Warshauer; Mathematical Explorations, Stipes Publishing, Champaign, IL, 2006.
• Max L. Warshauer, Joyce Fischer; Mathworks: An Innovative Approach to Systemic Change in Mathematics Education, The Journal of the Society of Educators and Scholars, Carolyn Morales, Chief Editor, Inter American University of Puerto Rico, Metropolitan Campus, San Juan, Puerto Rico, March 26, 2003.
• Max L. Warshauer; Mathematical Explorations, Mathematics Informatics Quarterly, Vol. 13, No. 1, March 2003.
• Max L. Warshauer, Willie Yong, Agus Susanta; Geometric Explorations with the Geometer's Sketchpad; Menemui Matematik (Discovering Mathematics), Vol. 25, No. 1, 2003.
• Max L. Warshauer, K. Reinke; Mathworks: Preparing Young Hispanic Students for Algebra; 2003 Education Monograph Series, National Association of Hispanic and Latino Studies, Heritage and History: A Celebration of Diversity, Houston, Feb. 2003.
• Max L. Warshauer, Willie Yong; Arithmetic and Geometric Mean, Menemui Matematik (Discovering Mathematics), Vol. 24, No. 2, 2002, p. 17 -22.
• Max L. Warshauer, T. McCabe, D. Shapiro, and H. Warshauer; Discovering Discrete Mathematics, Level 4, Stipes Publishing, 2001.
• Max L. Warshauer, T. McCabe and D. Shapiro; Math Explorations, Level 3; with T. McCabe, D. Shaprio, and Stipes Publishing, 2001.
• Max L. Warshauer, Why Number Theory is an Ideal Subject for an Honors Course; with T. McCabe, The National Honors Report, Vol. XXII, No. 1, Spring 2001.
• Max L. Warshauer, H. Warshauer; Algorithms, Encyclopedia of Mathematics, Routledge Falmer, New York, London, 2001.
• Max L. Warshauer, H. Warshauer; Mathematics, Nature, Encyclopedia of Mathematics, Routledge Falmer, New York, London, 2001.
• Max L. Warshauer, T. McCabe and H. Warshauer; The Mathematical Mystery Tour, Level 1; Stipes Publishing, 2000.
• Max L. Warshauer, ; with T. McCabe and H. Warshauer; MathQuest, Level 2, Stipes Publishing, 2000.
• Max L. Warshauer, Math Reader Magazine for elementary students, 1998.
• Max L. Warshauer, Math Explorer Magazine for intermediate students, 1998.
• Max L. Warshauer, Different Approaches to Summer Programs; Summac Forum, Volume 3, Number 1, February, 1995.
• Paul A. Kennedy, Max L. Warshauer, and E. Curtin; Factoring by Grouping; with P. Kennedy and E. Curtin, Mathematics and Computer Education, Vol. 25, Number 2, Spring 1991.
• Don G. Hazlewood, M. Warshauer, and S. Stouffer; Suzuki Meets Polya; Teaching Algebra to Elementary School Children, with D. Hazlewood and S. Stouffer, The Arithmetic Teacher, Volume 37, Number 3, 1989.
• Max L. Warshauer, Conway's Parallel Sorting Algorithm; Journal of Algorithms, No. 7, 1986, p. 270-276.
• Max L. Warshauer, Canonical Localizers and Non-Maximal Orders in the Witt Setting, Journal of Number Theory, Volume 20, 1984, p. 81-9.
• Max L. Warshauer, Diagonalization up to Witt; Pacific Journal of Mathematics, Volume 98, No.2, 1982, p. 469-475.
• Max L. Warshauer, The Witt Group of Degree k Maps and Asymmetric Inner Product Spaces; Lecture Notes in Mathematics, 914, Springer Verlag, 1982.

Teaching Philosophy

The reason that I teach is because of the joy that comes from seeing my students realize that they each have the ability to contribute to society in so many ways.

I especially enjoy teaching Number Theory each year to students ranging from high school students in summer math camps to undergraduate music majors to graduate students in mathematics.  Number theory is ideally suited for students with different math backgrounds since the concepts are developed based on simple examples.  The key is to not take things for granted, to be clear about what we assume, and to encourage the students to become active participants in every class.  In this setting, I have found that all students are capable of amazing accomplishments; the challenge is to inspire students to realize how much they can do for themselves. 

My problem sets reflect this basic philosophy including problems to "Prove or Disprove and Salvage if Possible".  Numerical problems and examples lead to patterns that encourage studetns to make conjectures and question why things work.  The students see that not all of our conjectures are true and they develop the ability to make new discoveries for themselves.  Math class is not just a time for me to lecture the students, but a time when students can discuss their proofs and learn from one another by working together.  In mathematics, there arre often multiple ways to do a problem and discussing mathematics with others enables students to understand the subtle, simple ideas that can lead to new discoveries.  The best way to learn an ideaas is to explain what you are doing to someone else.  The process of having students explain their proofs in class helps all students learn more. 

Teaching mathematics involves much more than numbers and facts; it involves building character, instilling confidence, and nurturing a student's creativity and imagination.  Students develop a foundation that will enable them to analyze problems critically in any area with a passion for learning and a deep understanding of how working together they can solve problems that alone may have seemed insurmountable.