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Lincoln Bridge



Bridge to Higher Mathematics     MA 1971   D21

Joseph D. Fehribach


Course Policies and General Information




Martin Aigner & Günter M. Ziegler

Proofs from THE BOOK, 6thed.,

Springer-Verlag, 2018.




Syllabus of Homework Assignments



       1 Due  Tuesday   30March2021 # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
       2 Due  Tuesday     6April2021 # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
       3 Due  Tuesday   13April2021 # 1, 2, 3, 4, 5
       4 Due  Friday       23April2021 # 1, 2, 3, 4
       5 Due  Tuesday     4May2021 # 1, 2, 3, 4



Quizzes


Blank Quizzes


Quiz Solutions




Final Exams



Videos

  

                       The Rules                                                                                           Statements, Predicates, Quantifiers




Implications, Theorems, Truth Tables




Types of Proofs, Negation




Set Containment, Contradiction, Complements




Set Differences, Power Sets, Cardinality




Induction, Transfinite Numbers




Set Theory Axioms




Set Construction, Induction Example




Peano Axioms, Infinitude of the Primes (Proof One, Start Proof Two)




Infinitude of the Primes (Finish Proof Two; Start Proof Four)




Infinitude of the Primes (Finish Proof Four)




Root 2 is Irrational; Fermat Sum of Two Squares Theorem




Lemma 1; Lemma 2




Lemma 3; Proof of Theorem




The Reals Are Not Countable




Continued Fractions: Example 1




Continued Fractions: Example 2




Continued Roots: Example 3, Means




Harmonic Mean ≤ Geometric Mean ≤ Arithmetic Mean




Basics of Graph Theory




The Euler Formula; The Four Color Problem




Four Color Theorem (Part 1)




Four Color Theorem (Part 2)




No Odd Cycle ==> No Odd Walk




Cauchy Sequences




Birthday Paradox




Review, Exam Discussion



JDF (E-Mail: bach@wpi.edu)
Last Updated: Monday 17 May 2021
Copyright 2013, 2015, 2021 Joseph D. Fehribach