[{"content":"Courses: Dr. Clair is on sabbatical for AY2025–26.\nOffice hours: Ritter 109 · By appointment only.\n","externalUrl":null,"permalink":"/","section":"","summary":"","title":"","type":"page"},{"content":"","externalUrl":null,"permalink":"/authors/","section":"Authors","summary":"","title":"Authors","type":"authors"},{"content":"","externalUrl":null,"permalink":"/categories/","section":"Categories","summary":"","title":"Categories","type":"categories"},{"content":" Web pages for my courses # Survey of Calculus Time Series ","externalUrl":null,"permalink":"/courses/","section":"","summary":"","title":"Courses","type":"page"},{"content":" Probability, Statistics, and Data: A Fresh Approach Using R: Textbook for a calculus based introductory statistics course with a data science emphasis. Math and the Art of M.C. Escher online textbook. STARS@SLU and STARS 2025. SLU Math Team: Training material and history. Courses Teaching Resources Recreational Math Course Web Pages # Math 120: College Algebra Math 130: Elementary Statistics with Computers Stat 1300: Elementary Statistics with Computers Math 132: Survey of Calculus Math 142: Calculus I Math 1520: Calculus II Math 1660: Discrete Mathematics Stat 2300: Intermediate Statistics Math 244: Calculus III Math 266: Principles of Mathematics Math 320: Numerical Analysis Math 355: Differential Equations Math 370: Advanced Math For Engineers Stat 3850: Foundations of Statistics Math 403: Probability and Statistics for Engineers Math 4050: History of Mathematics Math 451: Complex Analysis I Math 452: Complex Analysis II Stat 4840/5084: Time Series Stat 4880/5088: Bayesian Statistics and Statistical Computing Math 593: Graphs and Markov Chains Math 641-2: Differential Geometry I-II CS 150: Object Oriented Programming CS 220: Computer Science II EE/CS 305: Microprocessors CSCI 3500: Operating Systems CSCI 3820: Computer Graphics Math 110-111 (U. of Chicago, 1995-6). Teaching Resources # Slides for Tilings by Polygons for Girls, Inc., June 10, 2025. Slides for The Aperiodic Monotile, math club talk. Slides for Numbers in Clay, sample History of Math lecture. Slides for Standards Based Grading, colloquium at SLU, Jan 26, 2024. Slides for Using R: ggplot2 and dplyr, SLU 1818 Statistics Day, Nov 17, 2017. Materials for the workshop Learning to Teach Introductory Statistics with R, Sep. 28, 2017 at FTTC. Materials for the HS teacher workshop Using R for introductory statistics, Nov. 17, 2016. Slides from my MathFest 2015 talk about student art from Math and the Art of M.C. Escher. Recreational Math # Here\u0026rsquo;s a sheet of printable aperiodic \u0026ldquo;hat\u0026rdquo; monotiles and the R code to make it. Symmetry at the Cathedral - a page dedicated to symmetry groups found at the Cathedral Basilica of St. Louis. Slides for a talk about the logarithm of two: log2-mar-2015.pdf. X Goes First: Wild Tales of a Tic-Tac-Toe Grandmaster, published in Math Horizons, Vol 21, No. 4, April 2014. Slides for a talk about Tic-Tac-Toe: ttt-jan-2014.pdf. Pictures of all legal and rational moves, up to symmetry. Articles for Strange Horizons # Strange Horizons is an online magazine of speculative fiction. I wrote a series of general interest mathematics articles which appeared in the magazine.\nThe Fourth Dimension (Sep. 2002) (or, try the Portugese translation. Thanks, Marcelo!) Folding (Mar. 2002) Steganography: How to Send a Secret Message (Oct. 2001) The Biggest Numbers in the Universe (Apr. 2001) Habitrails and Asteroids: Topology From the Inside (Jan. 2001) ","externalUrl":null,"permalink":"/teaching/","section":"","summary":"","title":"Education","type":"page"},{"content":" SLU Auth SLU Math/Stat Pius XII, Catalog St. Louis Forecast, Local Radar ESPN Giants, McCovey ESPN Hoops, Cal, SLU XKCD Slashdot Slate BEQ ","externalUrl":null,"permalink":"/links/","section":"","summary":"","title":"Links","type":"page"},{"content":" I grew up in San Francisco, and went to Lowell High. I did math and computer science at Berkeley, then went to U. of Chicago for my PhD in math.\nI met my wife Elissa in Chicago. She taught special education for many years and is now a school psychologist. She maintains the world\u0026rsquo;s premiere Goat Allergy page.\nWe spent two years living in Brooklyn while I was working at the CUNY Graduate Center, then moved to St. Louis in 2000. Our two grown up kids Ben and Becca have left home and our two grown up cats Snickers and Lola have not.\nI play too little ultimate frisbee and too much Pokémon Go.\n","externalUrl":null,"permalink":"/personal/","section":"","summary":"","title":"Personal","type":"page"},{"content":"I write puzzles and organize puzzle events.\nOrganized the St. Louis Puzzled Pint from 2015-2020. Wrote most of the January 2018 - Stranger Things set. Wrote the September 2016 - Rats set. Wrote a Puzzled Pint style set in March 2020 called In Pour Taste that\u0026rsquo;s got some pretty dark pandemic humor. Different Area, Same Hunt: DASH. Wrote The Hole Story puzzle for DASH 10. Co-wrote the Monsters puzzle for DASH 7. Co-organized the St. Louis site for DASH 7 and DASH 8. Mathematical Puzzle Programs, an annual puzzle hunt for teams of high school students. I organize the SLU site. I wrote one puzzle for the 2019 edition. I was a major contributor to hunt design for the 2025 Izibalo and 2026 Where in the world\u0026hellip;. Here are some slides from a presentation about MaPP I gave at MathFest 2024. Wrote two St. Louis specific puzzles for The Octothorpean Order. Designed, built, and ran the Sensation escape room in 2014. Chestnuts: a collection of puzzles I\u0026rsquo;ve had on the web since the mid 1990\u0026rsquo;s. I didn\u0026rsquo;t create these, they\u0026rsquo;re well known! ","externalUrl":null,"permalink":"/puzzles/","section":"","summary":"","title":"Puzzles","type":"page"},{"content":" Projects # Optimal Strategies for Sports Betting Pools. The CLOP pool picks making package. A Mathematica package for drawing Penrose tilings: PenroseTiles.m, PenroseTiles.nb Slides for MEDC, 6/3/25 Papers # The Ihara Zeta Function of the Infinite Grid, The Electronic Journal of Combinatorics, Volume 21, Issue 2, 2014. Online version\nAbstract: The infinite grid is the Cayley graph of ZxZ with the usual generators. In this paper, the Ihara zeta function for the infinite grid is computed using elliptic integrals and theta functions. The zeta function of the grid extends to an analytic, multivalued function which satisfies a functional equation. The set of singularities in the domain is finite. The grid zeta function is the first computed example which is non-elementary, and which takes infinitely many values at each point of the domain.\nRelated Mathematica files: ComplexUtilities.m, GridZeta.m, GridZeta.nb. November 3, 2013 AMS Talk.\nZeta Functions of Graphs With Z Actions, Journal of Combinatorial Theory, Series B, Volume 99 #1, Jan 2009, p48-61. (Online version) | (Preprint version)\nAbstract: Suppose Y is a regular covering of a graph X with covering transformation group G = Z. This paper gives an explicit formula for the L² zeta function of Y and computes examples. When G = Z, the L² zeta function is an algebraic function. As a consequence it extends to a meromorphic function on a Riemann surface. The meromorphic extension provides a setting to generalize known properties of zeta functions of regular graphs, such as the location of singularities and the functional equation.\nWith David Letscher, Optimal Strategies for Sports Betting Pools, Operations Research 55 #6, Nov-Dec 2007, pp 1163-1177. pools-or.pdf Also see the Optimal Strategies for Sports Betting Pools page for more information, including reports on other seasons results.\nAbstract: Every fall, millions of Americans enter betting pools to pick the winners of each weekend\u0026rsquo;s football games. In the spring, NCAA tournament basketball pools are even more popular. In both cases, teams which are popularly perceived as \u0026ldquo;favorites\u0026rdquo; gain a disproportionate share of entries. In large pools there can be a significant advantage to picking upsets that differentiate your picks from the crowd.\nIn this paper we present a model of betting pools that incorporates opponent behavior. We use the model to derive strategies that maximize the expected return on a bet in both football and tournament style pools. These strategies significantly outperform strategies based on maximizing score or number of correct picks — often by orders of magnitude.\nWith Kevin Whyte, Growth of Betti numbers, Topology, volume 42, #5, p1125-1142 (2003). cw02_growth.pdf\nAbstract: Suppose X is any finite complex with vanishing L² Betti number. We prove upper bounds on the Betti numbers for regular coverings of X, sublinear in the order of covering. The bounds are sensitive to the Novikov-Shubin invariants of X, and are improved in the presence of a spectral gap.\nWith Shahriar Mokhtari-Sharghi, Convergence of zeta functions of graphs, Proceedings of the AMS, volume 130, #7, p1881-1886 (2002). cm00.pdf\nAbstract: The L²-zeta function of an infinite graph Y (defined previously in a ball around zero) has an analytic extension. For a tower of finite graphs covered by Y, the normalized zeta functions of the finite graphs converge to the L²-zeta function of Y.\nWith Shahriar Mokhtari-Sharghi, Zeta Functions Of Discrete Groups Acting On Trees, Journal of Algebra 237, p591-620 (2001). cm99_zeta.pdf\nAbstract: This paper generalizes Bass\u0026rsquo; work on zeta functions for uniform tree lattices. Using the theory of von Neumann algebras, machinery is developed to define the zeta function of a discrete group of automorphisms of a bounded degree tree. The main theorems relate the zeta function to determinants of operators defined on edges or vertices of the tree. A zeta function associated to a non-uniform tree lattice with appropriate Hilbert representation is defined. Zeta functions are defined for infinite graphs with a cocompact or finite covolume group action.\nResidual Amenability and the Approximation of L²-invariants, Michigan Math Journal 46(2), 1999. res_amenb.pdf\nAbstract: We generalize Luck\u0026rsquo;s Theorem to show that the L²-Betti numbers of a residually amenable covering space are the limit of the L²-Betti numbers of a sequence of amenable covering spaces. We show that any residually amenable covering space of a finite simplicial complex is of determinant class, and that the L² torsion is a homotopy invariant for such spaces. We give examples of residually amenable groups, including the Baumslag-Solitar groups.\nResidual Amenability and the Approximation of L²-invariants, PhD Thesis, U. of Chicago, June 1998. clair_thesis.pdf\n","externalUrl":null,"permalink":"/research/","section":"","summary":"","title":"Research","type":"page"},{"content":"","externalUrl":null,"permalink":"/series/","section":"Series","summary":"","title":"Series","type":"series"},{"content":"","externalUrl":null,"permalink":"/tags/","section":"Tags","summary":"","title":"Tags","type":"tags"}]