Introduction to Proofs

All of the material I’ve made for MAT102: Introduction to Proofs can be found here.

LaTeX: If you’re interested in the LaTeX source, please email me. I’m happy to share!

Videos

• YouTube Playlist

Slides

Summer 2020

• 0_Introduction
• 1_Number_systems
• 2_Divisibility
• 2_Even_Odd
• 3_Axioms
• 4_Mathematical_Statements
• 5_Truth_and_Falsity
• 6_Logical_Equivalence
• 7_Negation
• 8_Proof_Strategies_Direct_Contrapositive
• 9_Proof_Strategies_Contradiction
• 10_Sets_Intro
• 11_Sets_Constructions
• 12_Sets_Identities_and_counterexamples
• 13_Functions
• 14_Relations
• 15_Equivalence_relations
• 16_Equivalence_Classes
• 17_Inequalities_Axioms
• 18_Inequalities_AMGM
• 19_Inequalities_Triangle_Inequality
• 20_Functions_2
• 21_Sum_Product
• 22_Induction_Intro
• 23_Induction_variations
• 24_Induction_recursion
• 25_Strong_Induction
• 26_Binary_Representation
• 27_Injections_Surjections_Bijections
• 28_Inverse_functions
• 29_Compositions
• 30_Cardinality_Definitions
• 31_Cardinality_Examples
• 32_Countability_Intro
• 33_Countability_Diagonalization
• 34_Countability_Rationals
• 35_Power_Set
• 36_Paradoxes
• 37_Cantors_Theorem
• 38_Number_Theory_Division_Algorithm
• 39_Number_Theory_GCD_and_LCM
• 40_Number_Theory_Euclidean_Algorithm
• 41_Number_Theory_FTA

Assignments

Summer 2020

• MAT102_S2020_PS1 – Tex – MAT102_S2020_PS1_Solns
• MAT102_S2020_PS2 – Tex – MAT102_S2020_PS2_Solns
• MAT102_S2020_PS3 – Tex – MAT102_S2020_PS3_Solns
• MAT102_S2020_PS4 – Tex – MAT102_S2020_PS4_Solns
• MAT102_S2020_PS5 – Tex – MAT102_S2020_PS5_Solns
• MAT102_S2020_PS6 – Tex – MAT102_S2020_PS6_Solns

Fall 2019

• MAT102_F2019_PS1 – Tex – MAT102_F2019_PS1_Solns
• MAT102_F2019_PS2 – Tex – MAT102_F2019_PS2_Solns
• MAT102_F2019_PS3 – Tex – MAT102_F2019_PS3_Solns
• MAT102_F2019_PS4 – Tex – MAT102_F2019_PS4_Solns
• MAT102_F2019_PS5 – Tex – MAT102_F2019_PS5_Solns

Tutorials

Summer 2020

• MAT102_S2020_Tutorials

Fall 2019

• MAT102_F2019_Tutorials – Tex

Tests, Quizzes, and Final Exams

Summer 2020

• Quizzes
  • MAT102_S2020_Quiz_1 – Tex – MAT102_S2020_Quiz_1_Solns
  • MAT102_S2020_Quiz_2 – Tex – MAT102_S2020_Quiz_2_Solns
  • MAT102_S2020_Quiz_3 – Tex – MAT102_S2020_Quiz_3_Solns
  • MAT102_S2020_Quiz_4 – Tex – MAT102_S2020_Quiz_4_Solns
  • MAT102_S2020_Quiz_5 – Tex – MAT102_S2020_Quiz_5_Solns
• Final Exam
  • MAT102_S2020_FINAL_EXAM (No instructor solutions were made for the exam)

Fall 2019

• Test
  • MAT102_F2019_Test_v1 – Tex – MAT102_F2019_Test_v1_Solns
• Quizzes
  • MAT102_F2019_Quiz1_v1– Tex – MAT102_F2019_Quiz1_v1_Solns
  • MAT102_F2019_Quiz2_v1 – Tex – MAT102_F2019_Quiz2_v1_Solns
  • MAT102_F2019_Quiz3_v1 – Tex – MAT102_F2019_Quiz3_v1_Solns
  • MAT102_F2019_Quiz4_v1 – Tex – MAT102_F2019_Quiz4_v1_Solns
• Final Exam
  • MAT102_F2019_FINAL_Exam – MAT102_F2019_FINAL_Solns

Other Materials

• Fall 2019 – Exam Jam Handout –
  • MAT102_F2019_Exam_Jam_handout – MAT102_F2019_Exam_Jam_Solutions