Discrete Math

Discrete Mathematics – Curriculum Map 

Unit 1: Introduction to Discrete Math & Logic

Topics:

• What is discrete math? Applications in computer science, networking, and cryptography

• Statements, truth values, and logical connectives (and, or, not, if…then)

• Truth tables

• Logical equivalence and laws of logic

• Conditional, biconditional statements, and negations

Skills/Outcomes:

• Construct truth tables

• Evaluate logical statements

• Translate real-world statements into logical form

• Understand logical reasoning in problem-solving

Unit 2: Set Theory

Topics:

• Sets and subsets

• Venn diagrams

• Set operations: union, intersection, difference, complement

• Cartesian products

• Applications: organizing data, databases

Skills/Outcomes:

• Use set notation correctly

• Solve problems using Venn diagrams

• Apply set operations in real-world contexts
  
  

Unit 3: Counting & Probability

Topics:

• Basic counting principles

• Factorials and permutations

• Combinations

• Simple probability

• Applications in games, data analysis, and networks

Skills/Outcomes:

• Calculate permutations and combinations

• Solve probability problems using counting techniques

• Apply counting principles to real-world scenarios

• 
  

Unit 4: Graph Theory

Topics:

• Graphs, vertices, edges

• Types of graphs: directed, undirected, weighted

• Paths, circuits, connectedness

• Applications: social networks, computer networks, route planning

Skills/Outcomes:

• Draw and analyze graphs

• Identify connected components

• Solve basic graph problems (shortest path, connectivity)

Unit 5: Algorithms & Problem Solving

Topics:

• What is an algorithm?

• Step-by-step problem solving

• Simple sorting and searching algorithms

• Efficiency and complexity (basic understanding)

• Applications in computer science

Skills/Outcomes:

• Trace and write algorithms

• Solve problems with algorithmic thinking

• Understand efficiency in basic terms
  
  

Unit 6: Coding with Python

Topics:

• Introduction to Python programming

• Variables, data types, and input/output

• Loops, conditionals, and functions

• Lists, dictionaries, and simple data structures

• Applying Python to solve discrete math problems (logic, sequences, graphs, probability)

Skills/Outcomes:

• Write and debug basic Python programs

• Use Python to model discrete math problems

• Apply coding skills to real-world problem solving

• 
  

Unit 7: Number Theory & Cryptography

Topics:

• Divisibility, primes, factors

• Modular arithmetic

• Basic cryptography (Caesar cipher, substitution ciphers)

• Applications in computer security

Skills/Outcomes:

• Solve modular arithmetic problems

• Encrypt and decrypt messages using simple ciphers

• Apply number theory in real-world contexts
  
  

Unit 8: Review, Projects, and Real-World Applications

Topics:

• Comprehensive review of all units

• Interdisciplinary projects (e.g., networks, algorithms, coding, cryptography)

• Real-world applications: games, coding, scheduling, social networks

Skills/Outcomes:

• Integrate discrete math concepts

• Present a project demonstrating application of concepts

• Connect discrete math to daily life and technology