MATH 052: FUNDAMENTALS OF MATHEMATICS FALL 2011 Course Info

MATH 052: FUNDAMENTALS OF MATHEMATICS
FALL 2011
JOHN VOIGHT
Course Info
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Lectures: Monday, Wednesday, Friday, 10:40 a.m.–11:30 a.m.
Dates: 29 August 2011–7 December 2011
Room: Rowell 118
Course Record Number (CRN): 90863
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Instructor: John Voight
Office: 16 Colchester Ave, Room 207C
Phone: (802) 656-2271
E-mail: [email protected]
Instructor’s Office Hours: Mondays, 2:30–4:30 p.m.; Wednesdays, 9:00–10:00
a.m.; or just make an appointment!
• Course Web Page: http://www.cems.uvm.edu/~voight/52/
• Instructor’s Web Page: http://www.cems.uvm.edu/~voight/
• Prerequisites: Math 21 (corequisite).
• Required Text: Larry Gerstein, Introduction to Mathematical Structures and Proofs,
corrected edition, 1996.
• Grading: Homework will count for 40% of the grade. Class participation and preparedness will count for 10% of the grade. There will be two 50-minute exams that
will each count for 10% of the grade and one comprehensive final exam that will
count for 30% of the grade.
Homework
Typically, homework will be assigned each class and is due the next class. It will be
collected approximately once a week and late homework will not be accepted. The homework
assignments are posted on the course webpage.
We will go over homework in class, and after this discussion it will be collected. You may
take notes during this discussion but only if you use a red pen.
Be sure to show your work and explain how you got your answer. Correct but incomplete
answers will only receive partial credit. Part of the beauty of mathematics is in the elegance
of its proofs, and one goal of this course is for you to learn to write mathematics excellently.
Cooperation on homework is permitted (and encouraged), but if you work together, do
not take any paper away with you—in other words, you can share your thoughts (say on a
blackboard), but you have to walk away with only your understanding. In particular, write
the solution up on your own.
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Plagiarism, collusion, or other violations of the Code of Academic Integrity
(see http://www.uvm.edu/policies/student/acadintegrity.pdf)
will be referred to the The Center for Student Ethics and Standards.
Class participation and preparedness
You are expected to read the section before we cover it in class. Come with good questions!
Your participation and preparedness in class is essential for your success and will be assessed
accordingly.
You must come to my office at least once during the semester (such as during office hours).
Exams
Outside of exceptional circumstances, make-up exams will not be given. Please mark the
dates of exams (below) in your calendar.
Accommodation
Appropriate and fair accommodations will be provided for students with documented
special needs; please contact the ACCESS office (http://www.uvm.edu/~access/) directly
and early in the semester.
Students have the right to practice the religion of their choice. Each semester students
should submit in writing by the end of the second full week of classes their documented
religious holiday schedule for the semester.
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Syllabus
According to the “official” catalog description, we will cover:
Emphasizing proofs, fundamental mathematical concepts and techniques are
investigated within the context of number theory and other topics.
• Chapter 1: Logic
– 1, 29 Aug (M): Hurricane Irene
– 2, 31 Aug (W): Introduction, §1.1: Statements, Proposition, and Theorems
– 3, 2 Sep (F): §1.2: Logical Connectives and Truth Tables
3 Sep (M): No class, Labor Day
– 4, 7 Sep (W): §1.3: Conditional Statements
– 5, 9 Sep (F): §1.4: Proofs: Structures and Strategies
– 6, 12 Sep (M): §1.5: Logical Equivalence
• Chapter 2: Sets, an introduction
– 7, 14 Sep (W): §2.1: Fundamentals
– 8, 16 Sep (F): §2.1, §2.2: Russell’s Paradox
– 9, 19 Sep (M): §2.3: Quantifiers
– 10, 21 Sep (W): §2.4: Set Inclusion
– 11, 23 Sep (F): §2.5: Union, Intersection, and Complement
– 12, 26 Sep (M): §2.6: Indexed Sets
– 13, 28 Sep (W): §2.7: The Power Set
– 14, 30 Sep (F): Review
• Exam 1, 3 Oct (M), covering material in §§1.1–2.5
• Chapter 2: Sets, continued
– 16, 5 Oct (W): §2.8: Ordered Pairs and Cartesian Products
– 17, 7 Oct (F): §2.9: Set Decomposition: Partitions and Relations
– 18, 10 Oct (M): §2.9
– 19, 12 Oct (W): §2.9
– 20, 14 Oct (F): §2.10: Mathematical Induction and Recursion
– 21, 17 Oct (M): §2.10
• Chapter 3: Functions
– 22, 19 Oct (W): §3.1: Definitions and Examples
– 23, 21 Oct (F): §3.2: Surjections, Injections, Bijections, Sequences
– 24, 24 Oct (M): §3.2
– 25, 26 Oct (W): §3.3: Composition of Functions
– 26, 28 Oct (F): §4.1: Cardinality: Fundamental Counting Principles
– 27, 31 Oct (M): Review
• Exam 2, 2 Nov (W), covering material in §§2.6–3.3
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• Chapter 4: Finite and Infinite Sets
– 29, 4 Nov (F): §4.2: Comparing Sets, Finite or Infinite
– 30, 7 Nov (M): §4.3: Countable and Uncountable Sets
– 31, 9 Nov (W): §5.8: Binomial Coefficients
• Chapter 6: Number Theory
– 32, 11 Nov (F): §6.1: Operations
– 33, 14 Nov (M): §6.2: The Integers: Operations and Order
– 34, 16 Nov (W): §6.3: Divisibility: The Fundamental Theorem of Arithmetic
– 35, 18 Nov (F): §6.3
21–25 Nov (M–F): No class, Thanksgiving Recess
36, 28 Nov (M): §6.4: Congruence; Divisibility Tests
37, 30 Nov (W): §6.5: Introduction to Euler’s Function
38, 2 Dec (F): §6.5
39, 5 Dec (M): §6.6: The Inclusion-Exclusion Principle, and Further Properties
of Euler’s Function
– 40, 7 Dec (W): Review
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• Comprehensive Final Exam: Monday, December 12, 7:30 a.m.–10:15 a.m.
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