COURSE INFO
SCHEDULE
SYLLABUS
HOMEWORK
WRITING ASSIGNMENTS
OFFICE HOURS
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Math 260
Introduction to Higher Mathematics
Schedule
On Mondays, we will be presenting material from Donald Knuth's Surreal Numbers . Class members will be responsible, in partnerships, for leading the class discussions. On Tuesdays and Thursdays, we will be working through the modules in Edward Burger's Expanding the Frontiers of Mathematics.
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Monday, 1/14: |
Course Introductions and Mathematical Puzzlers
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Tuesday, 1/15: |
Presentations and Introduction to Proofs
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Thursday, 1/17: |
More Proofs: Introduction to Induction
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Tuesday, 1/22: |
Direct Proofs and Mathematical Induction
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Thursday, 1/24: |
The Dangers of Induction: Uniform Rabbits
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Monday, 1/28: |
Introduction to Surreal Numbers
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Tuesday, 1/29: |
Strong Induction and the Euclidean Algorithm
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Thursday, 1/31: |
More on Divisibility and Diophantine Equations
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Monday, 2/4: |
Surreal Numbers: Transitivity and Induction on Day Sums
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Tuesday, 2/5: |
Unique Factorization, Integers, Units
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Thursday, 2/7: |
Fractions and Rationality
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Monday, 2/11: |
Surreal Numbers: Total Ordering, `Less Than', and Solving for New Numbers
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Tuesday, 2/12: |
Irrationality of e , general irrational numbers, Divisor Sets
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Thursday, 2/14: |
Sets, Intersections, Unions, Functions
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Tuesday, 2/19: |
One to One and Onto Functions, The 'Dry Cleaner' Theorem
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Thursday, 2/21: |
Cardinality, Number, Countability
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Monday, 2/25: |
Surreal Numbers: Assigning values to numbers
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Tuesday, 2/26: |
Power Sets: Higher Concepts of Infinity
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Thursday, 2/28: |
Nomenclature Paradoxes
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Monday, 3/3: |
Surreal Numbers: Generating Integers and Fractions
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Tuesday, 3/4: |
Pigeon Hole Principle, Review
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Thursday, 3/7: |
Midterm
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Monday, 3/24: |
Surreal Numbers: Our role as Mathematicians
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Tuesday, 3/25: |
Pigeon Hole Principle, Introduction to counting Problems
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Thursday, 3/27: |
The Binomial Theorem: Pascal's Triangle
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Monday, 3/31: |
Surreal Numbers: Addition, Calculation of the Day of Creation
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Tuesday, 4/1: |
Probability Exercises, Axioms, Intuition and Counterintuition
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Thursday, 4/3: |
Probability, Counting, The Monty Hall Problem
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Monday, 4/7: |
Surreal Numbers: The Aleph Day: Concepts of Infinity and Epsilon
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Tuesday, 4/8: |
Graphs, Connectivity, Eulerian Circuits
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Thursday, 4/10: |
Trees, Forests, Equivalent Characterizations
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Thursday, 4/17: |
Complete Graphs, Bipartite Graphs, Planar Drawings of Graphs
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Monday, 4/21: |
Surreal Numbers: Ancestral Sequences, Bigger and Bigger Infinities
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Tuesday, 4/22: |
Maximizing Edges in Planar Graphs, Symmetries of the Square
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Thursday, 4/24: |
Groups: Examples and Facts
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Monday, 4/28: |
Surreal Numbers: Wrap up
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Tuesday, 4/29: |
Introduction to Analysis, Sets. Openness and Closure
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Thursday, 5/1: |
More on Sets, Continuity
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Monday, 5/5 : |
Course Review
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