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Dr. Edward Burger is a professor mathematics at Williams College in Williamstown, MA. He received his BA from Connecticut College and his PhD from University of Texas at Austin.
He has received numerous awards including: the Nelson Bushnell Prize, for Scholarship and Teaching, Williams College, being listed among the top 100 best Math Teachers in the "100 Best of America", Reader's Digest's Annual Special Issue. He has also received the Award of Excellence, for "educational mathematics videos that break new ground", from Technology & Learning magazine.
His research interests include Algebraic Number Theory, Diophantine Analysis, padic Analysis, Geometry of Numbers, and the Theory of Continued Fractions.
An Introduction to Rigorous Thought
1.1 Silly Stories, Each with a Moral
Conundrums that Evoke Techniques of Effective Thinking
1.2 Nudges
Leading Questions and Hints for Resolving the Stories
1.3 The Punch Lines
Solutions and Further Commentary
1.4 From Play to Power
Discovering Strategies of Thought for Life
2. NUMBER CONTEMPLATION
2.1 Counting
How the Pigeonhole Principle Leads to Precision Through Estimation
2.2 Numerical Patterns in Nature
Discovering the Beauty of the Fibonacci Numbers
2.3 Prime Cuts of Numbers
How the Prime Numbers Are the Building Blocks of All Natural Numbers
2.4 Crazy Clocks and Checking Out Bars
Cyclical Clock Arithmetic and Bar Codes
2.5 Public Secret Codes and How to Become a Spy
Encrypting Information Using Modular Arithmetic and Primes
2.6 The Irrational Side of Numbers
Are There Numbers Beyond Fractions?
2.7 Get Real
The Point of Decimals and Pinpointing Numbers on the Real Line
3. INFINITY
3.1 Beyond Numbers
What Does Infinity Mean?
3.2 Comparing the Infinite
Pairing Up Collections via a One-to-One Correspondence
3.3 The Missing Member
Georg Cantor Answers: Are Some Infinities Larger than Others?
3.4 Travels Toward the Stratosphere of Infinities
The Power Set and the Question of an Infinite Galaxy of Infinities
3.5 Straightening Up the Circle
Exploring the Infinite Within Geometrical Objects
4. GEOMETRIC GEMS
4.1 Pythagoras and His Hypotenuse
How a Puzzle Leads to the Proof of One of the Gems of Mathematics
4.2 A View of an Art Gallery
Using Computational Geometry to Place Security Cameras in Museums
4.3 The Sexiest Rectangle
Finding Aesthetics in Life, Art, and Math Through the Golden Rectangle
4.4 Soothing Symmetry and Spinning Pinwheels
Can a Floor Be Tiled Without Any Repeating Pattern?
4.5 The Platonic Solids Turn Amorous
Discovering the Symmetry and Interconnections Among the Platonic Solids
4.6 The Shape of Reality?
How Straight Lines Can Bend in Non-Euclidean Geometries
4.7 The Fourth Dimension
Can You See It?
5. CONTORTIONS OF SPACE
5.1 Rubber Sheet Geometry
Discovering the Topological Idea of Equivalence by Distortion
5.2 The Band That Wouldnt Stop Playing
Experimenting with the Möbius Band and Klein Bottle
5.3 Knots and Links
Untangling Ropes and Rings
5.4 Fixed Points, Hot Loops and Rainy Days
How the Certainty of Fixed Points Implies Certain Weather Phenomena
6. MODELING OUR WORLD THROUGH GRAPHS
6.1 Circuit Training
From the Königsberg Bridge Puzzle to Graphs
6.2 Feeling Edgy?
Exploring Relationships Among Vertices, Edges, and Faces
6.3 Plane Old Graphs
Drawing in the Plane and Coloring Maps
6.4 Networking
Using Graphical Models to Find the Shortest, Closest, and Cheapest
7. FRACTALS AND CHAOS
7.1 Images
Viewing a Gallery of Fractals
7.2 The Infinitely Detailed Beauty of Fractals
How to Create Works of Infinite Intricacy Through Repeated Processes
7.3 Between Dimensions
Can the Dimensions of Fractals Fall Through the Cracks?
7.4 Mysterious Art of Imaginary Fractals
Creating Julia and Mandelbrot Sets by Stepping Out in the Complex Plane
7.5 They Dynamics of Change
Can Change Be Modeled by Repeated Applications of Simple Processes?
7.6 Predetermined Chaos
How Repeated Simple Processes Result in Utter Chaos
8. TAMING UNCERTAINTY
8.1 Chance Surprises
Some Scenarios Involving Chance That Confound Our Intuition
8.2 Predicting the Future in an Uncertain World
How to Measure Uncertainty Using the Idea of Probability
8.3 Random Thoughts
Are Coincidences as Truly Amazing as They First Appear?
8.4 Down for the Count
Systematically Counting All Possible Outcomes
8.5 Drizzling, Defending, and Doctoring
Probability in Our World and Our Lives
9.1 Stumbling Through a Minefield of Data
Inspiring Statistical Concepts Through Pitfalls
9.2 Getting Your Data to Shape Up
Organizing, Describing, and Summarizing Data
9.3 Looking at Super Models
Mathematically Described Distributions
9.4 Go Figure
Making Inferences from Data
9.5 War, Sports, and Tigers
Statistics Throughout Our Lives
10. DECIDING WISELY
Applications of Rigorous Thinking
10.1 Great Expectations
Deciding How to Weigh the Unknown Future
10.2 Risk
Deciding Personal and Public Policy
10.3 Money Matters
Deciding Between Faring Well and Welfare
10.4 Peril at the Polls
Deciding Who Actually Wins an Election
10.5 Cutting Cake for Greedy People
Deciding How to Slice Up Scarce Resources
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