Precalculus knowledge for learning Discrete Math CS topics?

In summary, in order to understand the Discrete Mathematics chapters recommended for Computer Science, one should have a strong understanding of topics such as integer exponents, polynomials, rational expressions, equations, functions, and matrices from Precalculus. Additionally, knowledge of symmetry and transformations, complex numbers, exponential and logarithmic functions, and combinatorics would also be beneficial.
  • #1
eindoofus
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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
Code:
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 Langauge and Grammars
12.2 Finite-State Machines with Output
12.3 Finite-State Machines with No Output
12.4 Langauge Recognition
12.5 Turing Machines
Precalculus
Code:
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
To adequately answer this question, one should know the topics in Precalculus that are related to the topics in Discrete Mathematics for Computer Science. These include: - Integer Exponents and Order of Operations - Polynomials and Factoring - Rational Expressions - Equation Solving - Functions, Graphs, and Graphers - Linear Functions, Slope, and Applications - Symmetry and Transformations - Zeros of Linear Functions and Models - Complex Numbers - Zeros of Quadratic Functions and Models - Analyzing Graphs of Quadratic Functions - Polynomial Functions and Modeling - Polynomial Division and The Remainder and Factor Theorems - Theorems about Zeros of Polynomial Functions - Rational Functions - Composite and Inverse Functions - Exponential Functions and Graphs - Logarithmic Functions and Graphs - Properties of Logarithmic Functions - Systems of Equations - Matrices and Matrix Operations - Inverses of Matrices - Partial Fractions - Parabola, Circle, Ellipse, Hyperbola - Sequences and Series - Arithmetic and Geometric Sequences and Series - Mathematical Induction - Combinatorics - The Binomial Theorem - Probability
 

1. What is the purpose of learning precalculus in preparation for studying discrete math in CS?

Precalculus is a fundamental branch of mathematics that covers topics such as algebra, trigonometry, and geometry. These concepts are essential for understanding the more complex mathematical concepts in discrete math, which is heavily used in computer science. Having a strong foundation in precalculus will make it easier to grasp and apply the concepts in discrete math, ultimately helping students become better problem solvers in the field of computer science.

2. What are the key concepts and skills from precalculus that are necessary for understanding discrete math?

Some of the key concepts and skills from precalculus that are necessary for understanding discrete math include functions, equations, inequalities, matrices, logarithms, and trigonometry. These concepts are used to model real-world problems and analyze data, which are crucial skills in computer science.

3. How does precalculus relate to discrete math in terms of problem-solving and critical thinking?

Precalculus and discrete math both involve problem-solving and critical thinking, but they approach it in different ways. Precalculus deals with continuous functions and real numbers, while discrete math deals with discrete structures and finite sets. However, both require logical thinking, abstraction, and the ability to break down complex problems into smaller, more manageable parts.

4. Is it possible to study discrete math in CS without a strong background in precalculus?

While it is possible to study discrete math in CS without a strong background in precalculus, it may be more challenging. Precalculus lays the foundation for understanding the more advanced concepts in discrete math, and not having a solid understanding of precalculus may lead to difficulties in comprehending and applying these concepts.

5. Are there any resources or methods you recommend for improving precalculus knowledge for learning discrete math in CS?

Some helpful resources for improving precalculus knowledge for learning discrete math in CS include textbooks, online courses, and practice problems. It is also beneficial to work on strengthening your algebra and trigonometry skills, as these are essential components of precalculus. Additionally, seeking help from a tutor or participating in study groups can also be beneficial for understanding and applying precalculus concepts.

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