Ed Barbeau

Office: Bahen Centre/BA 6176 Email: barbeau@math.toronto.edu Phone: (416) 653-1961

• For teachers
• For undergraduates
• For secondary students
• For latest olymon

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Ed Barbeau is professor emeritus of mathematics at the University of Toronto.

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Talks, articles and compilations

• The Matching Game
• Intuition and Rigour
• Proof in Mathematics (with G. Hanna)
• Problems for school students and their parents (OAME 2007)
• Preparation for further mathematical study
• The Dr. Fox effect
• Egerton Ryerson on mathematics instruction in schools
• Classic puzzles old and new
• An elementary combinatorial investigation
• Composing linear polynomials
• Composing quadratic and higher degree polynomials
• How close are products of consecutive integers to squares?
• Mathematics in modern society
• Problems and solutions
• Notes on quadratic and cubic allemands
• Gregarious and reclusive triples

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Book reviews

• C. Alsina & R.B. Nelson: Icons of mathematics
• P. Borwein, P. Liljedahl, H. Zhai (eds): Mathematicians on creativity
• A. Cuoco & J.J. Rotman: Learning mathrmatics/R. Irving: Beyond the quadratic function
• R. Dahlke: How to succeed in college mathematics
• J. Havil: Surprising solutions to counterintuitive conundrums
• J. Havil: The irrationals
• R. Honsberger: Mathematical delights
• Liping Ma: Knowing and teaching elementary mathematics
• S. Rabinowitz & M/ Bowron: Index to mathematical problems
• J. Rosenhouse: The Monty Hall problem
• S. Simonson: Rediscovering mathematics 1975-1979

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Aftermath columns in the Frontenac News

• Crossing the River (July 25, 2013)
• Life's Big Questions {August 15, 2013)
• Neat games for two people (August 22. 2013)
• The number 142857 (September 5, 2013)
• Some birthday surprises {September 19, 2013)
• The convenience store (October 17. 2013)
• Convenience store revisited (October 31, 2013)
• Frog jump {November 21, 2013)
• Pythagorean triples (December 5. 2013)
• A magic square (December 19, 2013)
• The richness of mathematics (January 9, 2014)
• Divisibility (January 23, 2014)
• The problem of the four points (February 5, 2014)
• Matchmaking (February 27, 2014)
• Red and green hats (March 20, 2014)
• Challenge with digits (March 27, May 1, May 8, 2014)
• The birthday cake (April 10, 2014)
• The problem of the large number (May 22, 2014)
• A pair of geometry problems (June 5, June 19, 2014)
• The ace rises to the top (July 3, 2014)
• The art of sitting and standing (July 17, 2014)
• The ratchet (July 31, 2014)
• The beer mug theorem (August 14, 2014)
• The beer mug theorem: diagram (August 14, 2014)
• The arithmetic games (August 21, 2014)
• The rotating table (September 18, 2014)
• A problem for this year (October 9, 2014)
• Summing cubes (October 16, 2014)
• The journey of Ardeth and Charlotte (November 6, 2014
• Billiard balls (November 27, 2014)
• Noughts and crosses (December 4, 2014)
• Jack, the hunter (December 18, 2014; January 8, 2015)
• Counting the zeros (January 15, 2015)
• The ten number surprise (January 29, 2015)
• The four colour theorem (February 12, 2015)
• Extra-sensory perception (February 26, 2015)
• A game for two (March 12, 2015)
• Dodecabus (March 26, 2015)
• The turnaround (April 9, 2015)
• Reproducing squares (April 30, 2015)
• Confidence in mathematics (May 14, 2015)
• Horses and Egyptian fractions (June 4, 2015)
• Homer Simpson and Fermat's Last Theorem (June 25, 2015)
• GIMPS and the prime from hell (July 9, 2015)
• Two problems about numbers (July 23, 2015)
• The Alabama paradox (August 6, 2015)
• Knights and knaves (August 27, 2015)
• Rule of Eleven (September 17, 2015)
• Matt. 20:1-16 slightly revised (October 1, 2015)
• It makes no difference (October 29, 2015)
• Lines through points (November 12, 2015)
• Running it backwards (December 3, 2015)
• More digit puzzles (December 17, 2015)
• Palindromic products and some digital solutions (January 14, 2016)
• The last three holiday problems (January 21, 2016)
• In my estimation (February 11, 2016)
• Don't be confounded by compounding (February 25, 2016)
• An organized shuffle (March 17, 2016)
• A sequence of squares (April 28, 2016)
• The last ones standing (May 26, 2016)
• Cuckoo clock (June 2, 2016)
• Bridge on the River Tay (June 9, 2016)
• A microworld series (June 23, 2016)
• Cribbage (July 14, 2016)

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Links for elementary teachers

• Books for elementary pupils
• Exercises on arithmetic
• Exercises on ratio and proportion (percentages, rates)
• Exercises on patterns
• Exercises on combinatorics
• Exercises on geometry
• Mathematics in a deck of cards
• International Mathematical Talent Search

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Vignettes: links for elementary and secondary teachers

• The four points
• The law of cosines
• Fun with pythagoras
• Quadratic forms
• A magic square
• Passacaglia on an odd theme
• Reducible quadratics
• Squares of the form ab+k
• Number rings
• Products of integers that are powers
• Can products of consecutive numbers be square?
• A minimization example
• Prague clock sequences
• Consecutive multiples following consecutive squares
• Sums and multiples using all the digits
• Polynomials with no positive roots
• Polynomials: Cauchy radius
• The theatre line problem
• Interlocking pair sums and products
• Square-pair numbers
• The $4/n$ problem
• Products equal to sums
• Triangles with 60 and 120 degree angles
• Round robin tournaments
• Two periodic sequences
• Sets of integer additions
• Commuting exponentials
• A mixed-degree diophantine equation
• Harmonious quartets
• A cubic form
• Powers of 2, 5 and 10
• Oblong numbers
• Congenial and reclusive triples
• A collection of patterns

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Links for secondary teachers

• Preparation for university
• Problems in logic and analysis
• Exercises on factoring differences of squares
• The quadratic formula
• The inverse of a quadratic function
• Exercises on quadratic polynomials
• Exercises and problems on complex numbers
• Grade 12 calculus: The Plank Problem
• Arithmetic-geometric means inequality
• Area under a cycloid
• Angle subtended by a diamenter
• Pythagorean triples generalized
• Simultaneous equations with an extraneous solution
• Mathematics in a deck of cards

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Links for Ontario Grade XIII examination papers

• Algebra 1956
• Geometry 1956
• Trigonometry and Statics 1956
• Problems 1942
• Problems 1943
• Problems 1944
• Problems 1945
• Problems 1946
• Problems 1947
• Problems 1948
• Problems 1949
• Problems 1950
• Problems 1951
• Problems 1952
• Problems 1953
• Problems 1954
• Problems 1955
• Problems 1956
• Problems 1957
• Problems 1958
• Problems 1959
• Problems 1960
• Problems 1961
• English Composition 1956

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Links for undergraduate students

• Books on mathematicians
• Putnam and other problems sorted according to topic
• Putnam problems in algebra
• Putnam problems in calculus and analysis
• Putnam problems in combinatorics
• Putnam problems in differential equations
• Putnam problems in geometry
• Putnam problems in groups, fields and axiomatics
• Putnam problems in inequalities
• Putnam problems in matrices and linear algebra
• Putnam problems in number theory
• Putnam problems in probability
• Putnam problems in real numbers
• Putnam problems in sequences
• U of T Undergraduate Competition Student Rankings
• U of T Undregraduate Competitions: Complete problem set
• First University of Toronto Undergraduate Mathematics Contest (2001)
• Second University of Toronto Undergraduate Mathematics Contest (2002)
• Third University of Toronto Undergraduate Mathematics Contest (2003)
• Fourth University of Toronto Undergraduate Mathematics Contest (2004)
• Fifth University of Toronto Undergraduate Mathematics Contest (2005)
• Sixth University of Toronto Undergraduate Mathematics Contest (2006)
• Seventh University of Toronto Undergraduate Mathematics Contest (2007)
• Eighth University of Toronto Undergraduate Mathematics Contest (2008)
• Ninth University of Toronto Undergraduate Mathematics Contest (2009)
• Tenth University of Toronto Undergraduate Mathematics Contest (2010)
• Eleventh University of Toronto Undergraduate Mathematics Contest (2011)
• Twelfth University of Toronto Undergraduate Mathematics Contest (2012)
• Thirteenth University of Toronto Undergraduate Mathematics Contest (2013)
• Fourteenth University of Toronto Undergraduate Mathematics Contest (2014)
• Fifteenth University of Toronto Undergraduate Mathematics Contest (2015)
• Sixteenth University of Toronto Undergraduate Mathematics Contest (2016)
• Seventeenth University of Toronto Undergraduate Mathematics Contest (2017)
• Eighteenth University of Toronto Undergraduate Mathematics Contest (2018)
• Nineteenth University of Toronto Undergraduate Mathematics Contest (2019)
• Twentieth University of Toronto Undergraduate Mathematics Contest (2020)
• Twenty-first University of Toronto Undergraduate Mathematics Contest (2021)
• Twenty-second University of Toronto Undergraduate Mathematics Contest (2022)
• Twenty-third University of Toronto Undergraduate Mathematics Contest (2023)

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Polynomial Excursions

• Preface and foreword
• 1. Roots of Polynomials
• 2. The Taylor Expansion
• 3. Locating Zeros of Polynomials
• 4. Interpolation and Representation
• 5. Approximatiom by Polynomials
• 6. Irreducibility and Factorization
• 7. Dynamical Systems
• 8. Curves in the Plane
• 9. Allemands
• 10. Diophantine Equations
• 11. Diophantine Equations for Polynomials
• References: Books
• References: Papers

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Links for secondary students

I am grateful to M. Jean-David Houle for providing French translations for the Tips for Writing up Solutions.

• Tips for writing up solutions
• En 'ecrivant les solutions
• List of Olymon problems 1-300
• List of Olymon problems 301-600
• List of Olymon problems 601-present
• Olymon Volume 1 (2000)
• Olymon Volume 2 (2001)
• Olymon Volume 3 (2002)
• Olymon Volume 4 (2003)
• Olymon Volume 5 (2004)
• Olymon Volume 6 (2005)
• Olymon Volume 7 (2006)
• Olymon Volume 8 (2007(
• Olymon Volume 9 (2008)
• Olymon Volume 10 (2009)
• Olymon Volume 11 (2010)
• Olymon for January, 2008
• Olymon for March, 2008
• Olymon for April, 2008
• Olymon for May, 2008
• Olymon for July, 2008
• Olymon for September, 2008
• Olymon for October, 2008
• Olymon for November, 2008
• Olymon for December, 2008
• Olymon for January, 2009
• Olymon for February, 2009
• Olymon for March, 2009
• Olymon for April, 2009
• Olymon for May, 2009
• Olymon for June, 2009
• Olymon for August, 2009
• Olymon for October, 2009
• Olymon for November, 2009
• Olymon for January, 2010
• Olymon for February, 2010
• Olymon for March, 2010
• Olymon for May, 2010
• Olymon for June, 2010

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Report for Topic Study Group 4 at ICME-10 (2004)

• The report