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Thread: Precalculus knowledge for learning Discrete Math CS topics?

  1. #1
    Dec 2010

    Precalculus knowledge for learning Discrete Math CS topics?

    Below I've listed the chapters from a Precalculus book as well as the author recommended Computer Science chapters from a Discrete Mathematics book.

    Although these chapters are from two specific books on these subjects I believe the topics are generally the same between any Precalc or Discrete Math book.

    What Precalculus topics should one know before starting these Discrete Math Computer Science topics?:

    Discrete Mathematics CS Chapters
    1.1 Propositional Logic
    1.2 Propositional Equivalences
    1.3 Predicates and Quantifiers
    1.4 Nested Quantifiers
    1.5 Rules of Inference
    1.6 Introduction to Proofs
    1.7 Proof Methods and Strategy
    2.1 Sets
    2.2 Set Operations
    2.3 Functions
    2.4 Sequences and Summations
    3.1 Algorithms
    3.2 The Growths of Functions
    3.3 Complexity of Algorithms
    3.4 The Integers and Division
    3.5 Primes and Greatest Common Divisors
    3.6 Integers and Algorithms
    3.8 Matrices
    4.1 Mathematical Induction
    4.2 Strong Induction and Well-Ordering
    4.3 Recursive Definitions and Structural Induction
    4.4 Recursive Algorithms
    4.5 Program Correctness
    5.1 The Basics of Counting
    5.2 The Pigeonhole Principle
    5.3 Permutations and Combinations
    5.6 Generating Permutations and Combinations
    6.1 An Introduction to Discrete Probability
    6.4 Expected Value and Variance
    7.1 Recurrence Relations
    7.3 Divide-and-Conquer Algorithms and Recurrence Relations
    7.5 Inclusion-Exclusion
    8.1 Relations and Their Properties
    8.2 n-ary Relations and Their Applications
    8.3 Representing Relations
    8.5 Equivalence Relations
    9.1 Graphs and Graph Models
    9.2 Graph Terminology and Special Types of Graphs
    9.3 Representing Graphs and Graph Isomorphism
    9.4 Connectivity
    9.5 Euler and Hamilton Ptahs
    10.1 Introduction to Trees
    10.2 Application of Trees
    10.3 Tree Traversal
    11.1 Boolean Functions
    11.2 Representing Boolean Functions
    11.3 Logic Gates
    11.4 Minimization of Circuits
    12.1 Language and Grammars
    12.2 Finite-State Machines with Output
    12.3 Finite-State Machines with No Output
    12.4 Language Recognition
    12.5 Turing Machines
    R.1 The Real-Number System
    R.2 Integer Exponents, Scientific Notation, and Order of Operations
    R.3 Addition, Subtraction, and Multiplication of Polynomials
    R.4 Factoring
    R.5 Rational Expressions
    R.6 Radical Notation and Rational Exponents
    R.7 The Basics of Equation Solving
    1.1 Functions, Graphs, Graphers
    1.2 Linear Functions, Slope, and Applications
    1.3 Modeling: Data Analysis, Curve Fitting, and Linear Regression
    1.4 More on Functions
    1.5 Symmetry and Transformations
    1.6 Variation and Applications
    1.7 Distance, Midpoints, and Circles
    2.1 Zeros of Linear Functions and Models
    2.2 The Complex Numbers
    2.3 Zeros of Quadratic Functions and Models
    2.4 Analyzing Graphs of Quadratic Functions
    2.5 Modeling: Data Analysis, Curve Fitting, and Quadratic Regression
    2.6 Zeros and More Equation Solving
    2.7 Solving Inequalities
    3.1 Polynomial Functions and Modeling
    3.2 Polynomial Division; The Remainder and Factor Theorems
    3.3 Theorems about Zeros of Polynomial Funtions
    3.4 Rational Functions
    3.5 Polynomial and Rational Inequalities
    4.1 Composite and Inverse Functions
    4.2 Exponential Functions and Graphs
    4.3 Logarithmic Functions and Graphs
    4.4 Properties of Logarithmic Functions
    4.5 Solving Exponential and Logarithmic Equations
    4.6 Applications and Models: Growth and Decay
    5.1 Systems of Equations in Two Variables
    5.2 System of Equations in Three Variables
    5.3 Matrices and Systems of Equations
    5.4 Matrix Operations
    5.5 Inverses of Matrices
    5.6 System of Inequalities and Linear Programming
    5.7 Partial Fractions
    6.1 The Parabola
    6.2 The Circle and Ellipse
    6.3 The Hyperbola
    6.4 Nonlinear Systems of Equations
    7.1 Sequences and Series
    7.2 Arithmetic Sequences and Series
    7.3 Geometric Sequences and Series
    7.4 Mathematical Induction
    7.5 Combinatorics: Permutations
    7.6 Combinatorics: Combinations
    7.7 The Binomial Theorem
    7.8 Probability
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  2. #2
    MHF Contributor
    Sep 2012

    Re: Precalculus knowledge for learning Discrete Math CS topics?

    Hey eindoofus.

    The stuff in discrete math is not like the stuff in calculus: Discrete math deals with the exact opposite things that are dealt in calculus in which calculus deals with limits of all sorts and things that are continuous.

    I'd be at least prepared for chapter 1, 4, 5, and 7: it's not that you will directly use all the stuff in these chapters, but it will make understanding the new stuff a lot easier IMO.

    Basically one way to think about this, is that instead of looking at numbers and vectors, you are looking at specific kinds of structures that are based on sets and these structures will have a finite number of things in them where you look at relationships between the things and breaking down the whole set into parts and seeing what the implications of this are.

    This is the hardest thing for a lot of new students studying this because it is not like normal mathematics where you expect everything to be a number or a function: it starts from the idea that you have a collection of objects (i.e. a set) and then you put structure into the objects themselves (graphs, trees, languages, grammars, Turing Machines, etc) and then you break things apart slowly and steadily to understand them.
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