Fundamentals of Mathematics - Spring 2023

Lectures

Books

• Main Textbook: Lakins - The Tools of Mathematical Reasoning (Main Text)
• Supplement: LLM - Mathematics for Computer Science
• Supplement: Hutchings - Introduction to mathematical arguments
• Supplement: Hammack - Book of Proof

Links

• Dupuy - Math 52 - Fall 2017 (YouTube)
• LLM - Mathematics for Computer Science (YouTube)
  
• UVM Mathematics PhD Student Help Sessions (they only advertise as helping up to Calculus but these students know everything and generally are very helpful)
• Other fundamentals of mathematics pages (old exams, old homeworks, solutions)
• Taylor Dupuy - UVM -Fall 2017
• Jonathan Sands - UVM - Spring 2017
• John Voight - UVM - Fall 2012
• John Voight - UVM - Fall 2011

Quiz Schedule

• Quiz 01 (Monday 1/30/23, "I understand truth tables")
• Quiz 02 (Wednesday 2/1/23, "I understand how to read logic and convert between logic and English")
• Quiz 03 (Wednesday 2/8/23, Geometric Sum Formula + Difference of Powers)
• Quiz 04 (Friday 2/10/23, "I understand how to use basic properties of the integers to prove things")
• Quiz 05 (Friday 2/17/23, "I understand direct-proof techniques")
• Quiz 06 (Friday 3/3/23, "I understand indirect proof techniques")
• Quiz 07 (Friday 3/3/23, "I understand proofs by contradiction")
• Quiz Redos (Wednesday 3/8/23)
• Quiz 08 (Friday 3/31/23, "I understand proofs by induction")
• Quiz 09 (Friday 3/31/23, "I understand proofs by strong induction")
• Quiz 10 (Friday 4/7/23, "I understand the fundamental theorem of arithmetic")
• Quiz 11 (Friday 4/14/23, "I understand sets" - sec 4.1 )
• Quiz 12 (Friday 4/14/23, "I understand set membership" sec 4.2)
• Quiz 13 [ accidentally labelled Quiz 14 ](Friday 4/21/23, "I understand functions, domains, codomains, images, and preimages" sec 5.1, 5.2 )
• Quiz 14 (Friday 4/21/23, "I understand injectivity, surjectivity, and bijectivity" sec 5.3) Quiz 15 (Friday 4/21/23, "I understand functions on sets")
• Quiz 15 (Friday 4/28/23, "I understand function composition" sec 5.2) Quiz 14 (Friday 4/28/23, "I understand injectivity, surjectivity, and bijectivity" sec 5.3)
• Quiz 16 (TBD, "I understand modular arithmetic" )
• Quiz 17 (TBD, "I understand cardinality ")

• On Friday 4/21/23 I gave two quizzes labelled Quiz 14 and Quiz 15. The Quiz labelled "Quiz 14" was actually Quiz 13 and was just mislabelled. The quiz scheduled "Quiz 15", was about "understanding functions on sets" and was not originally scheduled. I will count this quiz in place of the scheduled Quiz 15 and give an extra quiz drop for the mix up. The true Quiz 14 is now scheduled to Friday 4/28/23 in place of the scheduled Quiz 15.
• The class voted to not have Quizzes 16 and 17 on Monday 4/24/23 so those were removed from the schedule.