Fundamentals of Mathematics - Spring 2024

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 (Friday, Feb 2 -- "I understand truth tables")
• Quiz 02 (Friday, Feb 2 -- "I understand how to read logic and convert between logic and English")
• Quiz 03 (Friday, Feb 9 -- Geometric Sum Formula + Difference of Powers)
• Quiz 04 (Friday, Feb 16 -- "I understand how to use basic properties of the integers to prove things")
• Quiz 05 (Friday, Feb 23 -- "I understand direct-proof techniques")
• Quiz 06 (Friday, March 1 -- "I understand indirect proof techniques")
• Quiz 07 (Friday March 1 -- "I understand proofs by contradiction")
• Quiz Redos (Wednesday, March 6)
• Quiz 08 (Friday, March 22 -- "I understand proofs by induction")
• Quiz 09 (Friday, March 29 -- "I understand proofs by strong induction")
• Quiz 10 (Friday, April 5 -- "I understand the fundamental theorem of arithmetic")
• Quiz 11 (Friday, April 19 -- "I understand how to show two sets are equal")
• Quiz 12 (Friday, April 26 -- "I understand functions, domains, codomains, images, and preimages")
• Quiz 13 ("I understand functions on sets")
• Quiz 14 ("I understand function composition")
• Quiz 15 ("I understand injectivity, surjectivity, and bijectivity" sec 5.3)
• Quiz 16 ("I understand modular arithmetic" )
• Quiz 17 ("I understand cardinality ")

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