Math 105 Mathematics as a Liberal Art Spring 2024

Prof.  Buckmire




POTD Homework


Exam Automathography








Unit 1: Numbers and Patterns
Monday January 22
#1: Introduction: Why Math? (CNBC, "Math-Challenged Americans...")
Wednesday January 24 #2: What is Mathematics? (Devlin's Prologue)
Friday January 26
#3: The Poison Game and Introduction to Modular Arithmetic
(Optional: A Primer on Modular Arithmetic)
Monday January 29
#4: Looking for Patterns In Numbers (Eves, Pythagorean Arithmetic)
Wednesday January 31
#5: Mathematical Induction (Gauss: The Child Genius)
Friday February 2
Mathematical Induction, continued
(Optional: Mathematical Induction)
Monday February 5
Wednesday February 7
#6: Looking for Numbers in Patterns
Optional (How UPC Bar Codes Work) and (ISBN FAQ)
Friday February 9
#7: Many Multiplications: An Algorithm Example
Optional videos (Grid Method), (Lattice method) and (3 Ways To Multiply)
Monday February 12
#8 The Fundamental Theorem of Arithmetic (& Prime Time)
Resource: Number Theory Handout and The First 1000 Primes
Optional (Ramunajan, Fermat's Little Thorem, Fermat' Last Theorem, Fifteen Theorem)
Resource: Fermat's Little Theorem calculator
Wednesday February 14
#9: All Numbers Are Not Rational!
Resource: Khan Academy video on Irrationality of \(\sqrt{2}\)
Friday February 16
Monday February 19
Presidents Day Holiday (No Class) 
Wednesday February 21
#10: All About That Base: Binary, Quinary and Septenary
Resource: Base Number Converter
Friday February 23
#11: Everything You Ever Wanted To Know About Hex
(Hexadecimal Color Wheel)
Unit 2: Logic, Proof and Infinity
Monday February 26 #12: Introduction to Logic: Truth Tables
Web Resource: Intro to Logic
Wednesday February 28 #13: Mathematical Logic: Implications

Web Reading (Wikipedia): Modus ponens and Modus tollens
 Reading: (Devlin, Truth Tables)
Friday March 1
#14: Mathematical Logic: Conclusions
Monday March 4
#15: Midterm Exam Review
Wednesday March 6
Midterm Exam
Friday March 8
Monday March 11 Spring Break
Wednesday March 13
Spring Break
Friday March 15
Spring Break
Monday March 18
16: Introduction to Infinite Sequences and Series
(Web Reading: Zeno's Paradox)
Wednesday March 20
17: Infinitesimals, Part 1: The Differential Calculus
Friday March 22
18: Infinitesimals, Part 2: The Integral Calculus
Monday March 25 19: The Fundamental Theorem of Calculus
Wednesday March 27 20: Power Sets, Infinite Sets, Bijections and Cardinality
(Reading on Transfinite Numbers)
Friday March 29 21: Aleph One and All That: The Continuum Hypothesis
Video: Comparing Infinite Sets, Numberphile's "Infinity is Bigger Than You Think"
Unit 3: Symmetry and Shapes
Monday April 1 22: Introduction to Symmetry and Shapes (Devlin on Symmetry Groups)
Wednesday April 3 23: Euclid, Geometry and The Platonic Solids
Video: Non-Euclidean Geometry
Web Resource: Platonic Solids Online
Friday April 5 24: Frieze (Strip) Patterns: Translational Symmetry
Web Resource:
Website on Frieze Patterns
Monday April 8 Class Cancelled
Wednesday April 10 #25: Euler and Graph Theory
Web Resource: The Euler Archive
Friday April 12 #26: Euler and Topology
Web Resource: Eulerian Graph and Hamiltonian Graph
Monday April 15 27: Tessellations: Tiling The Plane
Web Resource: New Pentagonal Tiling Found (2015). New "Einstein" Discovered/Created (March 2023).
Wednesday April 17 Class Cancelled
Friday April 19
Class Cancelled
Monday April 22
#28: Ambigrams
Wednesday April 24
Project Presentations
Friday April 26
Project Presentations
Monday April 29