Math 111, 2010

"Math 111" is the numerical designation of a course called Fundamentals of Mathematics. The course has three parts:

1. symbolic logic,
2. sets and relations,
3. the natural numbers.

There are several descriptions of this course on the web:

• department catalog
• expanded departmental description
• METU catalog

Instructors

section	place	time	instructor	office	office hours
§ 1	M 103	Mon 10:40–11:30, Wed 8:40–10:30	Ömer Küçüksakallı	141	Wed, Thurs 10:40–12:30
§ 2	M 104	Mon 11:40–12:30, Wed 13:40–15:30	David Pierce	222	(see my schedule)
§ 3	M 103	Tues 8:40–10:30, Thurs 12:40–13:30	Semra Pamuk	228	Tues–10:40–12:00, Thurs 10:40–12:30
§ 4	M 104	Mon 15:40–16:30, Wed 8:40–10:30	Ayşe Berkman	242

Assistants: Şükran Gül, Merve Gürbüz

Examinations

• Exam 1:
  • Solutions to Exam 1
  • Scores to Exam 1
  • Viewing hours for Exam 1 (possibly not yet ready)
• Exam 2 scores and viewing
• Final exam scores (papers can be seen on Monday, January 24, 10:00–12:00).

	date	time	weight	coverage	places
1st midterm	Tuesday, November 9	17.40	27 %	Pierce, §§ 2.0, 2, 3, 4, 6, 7, 8 (in part); 1.9; 3.0, 1; some topics are covered in Velleman, §§ 1.2–2.2 inclusive	M04 ABUKAN—AYAR M05 AYAZ—ÇELİK M06 ÇELİKTEN—GENÇ M07 GENLİK—KARACA M102 KARAGÜL—NURLU M103 NURMAMATOV—SANCAK M104 SARALAR—ÜZEL M105 YAĞLI—ZOBAR
2nd midterm	Monday, December 13	17.40	27 %	Cartesian products, relations, functions, equivalence relations, equipollence and countability. See Ömer Küçüksakallı's webpage for some exercises, and references in Velleman and Bloch. References also include Pierce, §§3.2, 3, 4, 6, 7, and 4.9. The main reference is your teacher's lectures.	M102 ABUKAN—AYAR M103 AYAZ—ÇELİK M104 ÇELİKTEN—GENÇ M105 GENLİK—KARACA M04 KARAGÜL—NURLU M05 NURMAMATOV—SANCAK M06 SARALAR—ÜZEL M07 YAĞLI—ZOBAR
final	TBA	TBA	36 %	the course!	see this pdf file
(instructor's discretion)			10 %

Make-up exam: January 22, at 13:30, in M-04, covering all topics.

Text

The main text for this course is your instructor's lectures. The electronic book Foundations of Mathematical Practice, by David Pierce, covers all topics of the course and more; it is available here (in 10-point type, each page intended for an A5 sheet of paper; this is the version of September 24, 2010):

• pdf
• ps
• dvi
• tex

Alternative references for some topics of the course include the following. Please don't start reading any of these books the night before an exam! Some of these books are easy reading, but do not cover everything we need in the course; other books here go far beyond the course.

• Ethan Bloch, Proofs and Fundamentals
• Stanley Burris, Logic for Mathematics and Computer Science
• Kevin Houston, How to Think Like a Mathematician (Türkçesi mevcuttur)
• Edmund Landau, Foundations of Analysis: The Arithmetic of Whole, Rational, Irrational, and Complex Numbers
• Matematik Dünyası dergisi:

  2003 IV

  Peano Belitleri, Sezgisel/Aksiyomatik Kümeler Kuramı*, Tümevarım

  2005 IV

  Sıralamalar

  2006 I

  Ordinaller*

  2006 II

  Seçim Beliti, Zorn Önsavı*

  2006 III

  Kardinaller, Cantor-Schröder-Bernstein Teoremi, Eşlenikler, Continuum Hipotezi

  2006 IV

  ℤ ve ℚ'nun inşaası

  2007 I, II

  Gerçel sayılar*

  (*: Starred topics are not covered in Math 111, but they are recommended for further reading.)
• Ali Nesin, Önermeler Mantığı
• Robert Stoll, Set Theory and Logic
• Patrick Suppes, Axiomatic Set Theory
• Alfred Tarski, Introduction to Logic and to the Methodology of Deductive Sciences
• Daniel Velleman, How to Prove It: A Structured Approach

Exercises

Reasonable exercises for Math 111 include the following (from the notes by Pierce unless otherwise stated):

• § 1.7: all.
• § 2.0: 1, 3.
• § 2.2: 1, 2, 4, 5.
• § 2.3: 1.
• § 2.4: 1, 2, 4, 5.
• § 2.6: all.
• § 2.7: 2, 5.
• Write formal proofs for the entailments in parts 5 and 6 of Lemma 2.7.8 and Exercises 2 and 5 of § 2.7 (using the System of Detachment defined in § 2.8).
• § 1.9: all.
• Exercises on quantifiers

Exercises from the Velleman book are § 1.1: 3, 4, 6; § 1.2: 8, 9, 12; § 1.5: 3, 5, 7.