Discrete Mathematics and Applications

Topic outline

• General

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• Subject Synopsis

  Subject Synopsis - Discrete Mathematics and Applications
  

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    Subject Synopsis File

• Number Theory 1

  1.1 Factorability

  1.2 Primes

  1.3 The Division Algorithm

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    Number Theory 1 File

• Number Theory 2

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  1.4 Greatest Common Divisors (GCD)

  1.5 Least Common Multiples (LCM)

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    Number Theory 2 File

• Number Theory 3

  1.6 Euclidean Algorithm

  1.7 Extended Euclidean Algorithm

  1.8 Modular Arithmetic

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    Number Theory 3 File

• Number Theory: Assessment
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    Number Theory: Assessment Quiz 1 File

• Sets

  2.1 Set Terminologies and Concepts

  2.2 Operation on Sets

  2.3 Cartesian Products

  2.4 Power sets

  2.5 Applications of sets theory

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    Sets File

• Functions

  2.6 Introduction to Functions

  2.7 One-to-One and Onto Functions

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    Functions File

• Relations

  2.8 Relations and Their Properties
  • Reflexive
  • Symmetric
  • Transitive

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    Relations File

• Sets, Functions and Relations: Assessment

  Sets, Functions and Relations: Assessment 
  

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    Sets, Functions and Relations: Assessment Quiz 2 File

• Assessment: Test 1

  Test 1
  

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    Assessment: Test 1 File

• Logic 1

  3.1 Propositional Logic
  

  3.2 Logical Connectives
  

  3.3 Propositional Equivalences
  

  
  

  
  

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    Logic 1 File

• Logic 2

  3.4 Predicates and  Quantifiers
  

  3.5 Rules of Inference
  

  
  

  
  

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    Logic 2 File

• Logic: Assessment
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    Logic: Assessment: Quiz 3 File

• Proof Techniques 1

  4.1 Direct Proof
  

  4.2 Indirect Proof
  

  4.3 Contradiction Method
  

  
  

  
  

  
  

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    Proof Techniques 1 File

• Proof Techniques 2

  4.4 Mathematical Induction
  

  4.5 Strong Induction and Well-Ordering
  

  
  

  
  

  
  

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    Proof Techniques 2 File

• Proof Techniques: Assessment
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    Logic: Assessment: Quiz 4 File

• Abstract Algebra 1

  Abstract Algebra 1
  

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    Abstract Algebra 1 File

• Abstract Algebra 2

  Abstract Algebra 2
  

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    Abstract Algebra 2 File

• Abstract Algebra 3

  Abstract Algebra 3
  

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    Abstract Algebra 3 File

• Abstract Algebra: Assessment

  Abstract Algebra: Assessment Quiz 5
  

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    Abstract Algebra: Assessment Quiz 5 File

• Assessment: Test 2

  Test 2

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    Assessment: Test 2 File

• Assessment: Final Exam

  Assessment: Final Exam
  

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    Assessment: Final Exam File