PDF Free Download A Brief Journey in Discrete Mathematics by Randolph Nelson

A Brief Journey in Discrete Mathematics

PDF Free Download | A Brief Journey in Discrete Mathematics by Randolph Nelson

Contents of Brief Journey in Discrete Mathematics

  • Introduction
  • Let Me Count the Ways
  • Permutations: With and Without Replacement
  • Dearrangements
  • Combinations: Without Replacement
  • Binomial Identities
  • Combinations with Replacement
  • Binomial-R Identities
  • Polynomial Solutions to Combinatorial
  • Problems
  • Transforms and Identities
  • Syntax Precedes Semantics
  • Stirling Numbers of the First Kind
  • Stirling Numbers of the Second Kind
  • The Stirling Transform and Inverse
  • Combinatorial Interpretation
  • Fearful Symmetry
  • Symmetric Functions
  • Simple Polynomials
  • The Quadratic Equation
  • Equation of the Minimum Distance Line
  • The Pythagorean Theorem
  • Cubic Polynomials
  • Elementary Symmetric Polynomials
  • Newton–Girard Formula
  • Identities and Combinatorial Coefficients
  • Inclusion–Exclusion
  • Fundamental Theorem of Symmetric Polynomials
  • Galois’ Theorem and Numerical Solutions
  • All That Glitters Is Not Gold
  • The Golden Ratio
  • Fibonacci Numbers
  • A Closed Form Solution
  • An Alternate Derivation
  • Generalized Fibonacci Numbers
  • k-Bonacci Numbers
  • Generalization of the Fibonacci Recurrence
  • Heads I Win, Tails You Lose
  • The Mathematical Model
  • Games That End Even
  • Catalan Numbers
  • Non-intuitive Results
  • The Correct Insight
  • Particular Sequences
  • Conclusions
  • Sums of the Powers of Successive Integers
  • A General Equation
  • Iterative Approach
  • Triangular Numbers
  • Cauchy’s Theorem
  • As Simple as + =
  • Modular Arithmetic
  • Fermat’s Little Theorem
  • Lagrange’s Theorem
  • Wilson’s Theorem
  • Cryptography
  • Hidden in Plain Sight
  • Properties of Prime Numbers
  • Properties of Integer Divisors
  • The Prime Counting Function
  • There Is Always a Prime Between n and n
  • The Prime Number Theorem with a
  • Controversy
  • Running Off the Page
  • Simple Continued Fractions
  • Periodic Simple Continued Fractions
  • Summary of Results
  • General Method to Create a Continued Fraction
  • Integer Quadratics and Quadratic Surds
  • Approximations Using Continued Fractions
  • Best Approximations
  • Lagrange’s Theorem and Historical Review
  • A Tools of the Trade
  • A Recurrence Relationships
  • A Adding Zero to an Equation
  • A Induction
  • A Contradiction
  • A Order of Summations
  • B Notation and Identities Derived in the Book
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PDF Free Download A Brief Journey in Discrete Mathematics by Randolph Nelson

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