Course Information

Course Textbook: A Transition To Advanced Mathematics, by D. Smith, M. Eggen, & R. St. Andre, 7th Edition, Brooks/Cole 2006 (ISBN: 0-495-56202-5; ISBN13: 978-0-495-56202-3). The prerequisite for 650:300 is Calculus II. This is a proofs-oriented course, so all of my quizzes and exams will be written so that you can complete them without a calculator.

There will be two examinations during the term, and a cumulative final. Please contact me TWO WEEKS prior to any exam if you have an excused absence. Weekly homework and quizzes will typically be due on Tuesdays. While I do not require attendance, you will be responsible for all the material covered in lecture, including announcements, changes to homework as well as the corresponding sections assigned from the text.

Grading Scheme: 100 HW/Quizzes, 200 Midterms (100 each), and 200 Final.

It is also important for you to know the Rutgers University Interim Academic Integrity Policy.

Suggested Exercises

Boldfaced exercises will be collected at the beginning of lecture. Pink exercises are bonus. I will select a subset of them to collect before each exam. Exercises listed are for the seventh edition of the book (maroon cover).

• 1.1 1, 2, 3 f h j, 4 b d f, 6 c e, 8 a, 9 c e, 10 a c, 11, 12 b c
• 1.2 1, 2 b c d e, 3 b d, 5 e f g, 6 f g h, 7 c d, 9 a b, 10 d e f, 12 b, 13, 14, 16 d
• 1.3 1 c f h i, 2 c f h i, 3, 6, 7 a, 8 a b c e, 9 a b g f, 10 b c d e, 12, 13 c d
• Please note that 08 Sep is on a MONDAY CLASS SCHEDULE
• 1.1 - 1.3 marked exercises due Tue 13 Sep (22 exercises + 1 bonus)
  
• 1.4 4 b d, 5 c d, 6 c e f, 7 e f h i k l, 8, 9 a e, 10, 11 b e
• 1.5 3 c d e, 4 c, 5 a c, 6 b d e, 7 a b, 8, 9, 10, 11, 12
• 1.6 1 b d h, 2 a c, 3, 4 a b c h i, 5 b, 6 d f i, 7 a, d, e
• 1.7 2 c f, 3 c, 4 c d, 5 a, 7 a, 9 c, 11 b, 14 b d, 18, 19, 21 a b c
• 1.4 - 1.7 marked exercises due 23 Sep (15 exercises + 3 bonus)
  
• 1.4 - 1.7 Quiz on 23 Sep. Solutions
  
  Supplementary Reading for Chapter 1
  1. Formal Logic: Its Scope and Limits, by Richard Jeffrey. McGraw Hill, Inc. 1991 (see Chapters 1 and 3)
  2. On Formally Undecidable Propositions of Principia Mathematica and Related Systems, by Kurt Godel, Transl. B. Meltzer. Dover Pub. 1992. This Dover edition is a translated publication of the original 1962 paper by Godel on the undecidability of certain propositions in a given axiomatic system. Not your usual weekend reading, but worth a look if you want to think hard.
  3. Professor Woodward's Math 300 Course Notes (please email me if you would like these lovely notes, exercises & solutions!)
  4. Elementary Number Theory, by David Burton. McGraw Hill, Inc. This is a very readable introduction to Number Theory and many of the exercises we have completed can be found in this textbook as well. Note that newer editions of this book are quite expensive and a first or second edition (the one I used) can be found online easily for less.
  5. An Introduction to the Theory of Numbers, by Ivan Niven and Herbert Zuckerman. John Wiley & Sons, Inc. The newest 1991 edition also has co-author Hugh Montgomery, but I have not looked at it myself. This is a slightly more advanced and broader treatment for a beginning Number Theory Course; it requires a little more work to read than the previous reference, but proves some more powerful results.
  
  
• 2.1 1 e f, 2, 3, 4 d f h j, 5 f j, 6 d, 7, 10, 13, 14 a b, 15 h, 16 d, 18
• 2.2 1 d f j, 2, 3 b e h, 5, 6 e, 9 a g h, 10 b, 11 c d, 12 d, 13 d, 15 c, 16 c, 18, 19
• 2.3 1 d g k l m n, 2, 4, 6 b, 7 a, 8 b c, 9 a, 10 d, 11 a, 12, 15 a b, 16, 17 b
• 2.4 1 c e, 2 c d, 4 f, 5 d e f g, 6 c f h k l, 7 d g l n o, 8 c f g h, 9 a, 10, 11, 12
• 2.1 - 2.4 marked exercises due Tue 11 Oct (36 exercises + 3 bonus)
  
• 2.5 1 a, 2, 4, 5, 6, 9, 10, 11
• 2.6 1 b d, 2 c d, 3, 6, 7, 9, 10, 15, 16 a, 17, 20, 22, 23
• 2.5 - 2.6 marked exercises due Fri 21 Oct (5 exercises + 4 bonus)
  
  Supplementary Reading for Chapter 2
  1. Introduction to Real Analysis, by Robert Bartle and Donald Sherbert. John Wiley & Sons, Inc. 1992 (see sections 1.1 and 1.3 for sets and induction).
  2. Basic Abstract Algebra, by Battacharya, Jain and Nagpaul, 2nd Ed. Cambridge University Press, 1996. Chapters 1 & 2 provide a compact discussion of sets and mappings, as well as integers, real and complex numbers.
  3. Abstract Algebra: An Introduction, by Thomas Hungerford. Following our discussion in class about possible uses of prime factorization, I am suggesting Chapters 12 and 14 on Public-Key Cryptography and Algebraic Coding Theory. This book also has a very nicely written appendix on Logic and Proof, Sets and Induction. Note that there is a much more advanced book by Hungerford, called Algebra, but I am recommending the undergraduate textbook.
  4. The Joy of Sets: Fundamentals of Contemporary Set Theory, by Keith Devlin. Springer Undergraduate Texts in Mathematics, 1993 (I think). The relaxed manner in which this book is written might make for some interesting and fun further reading in Set Theory. I have not used the book in a course myself, but have browsed through it.
  
  
• Professor Wilson's Math 300 Review Session 13:00-15:00, Sun 09 Oct, Hill 423.
  

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  Exam #1 covering Chapter 1 and 2.1 - 2.4 on Tue 11 Oct (in class). Sample of a midterm I gave the last time I taught Math 300 with solutions. Our exam solutions are here.

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• 3.1 2 b d f h, 3, 4 b d f g, 5 c e f g, 6 a c e i k l n p, 7 b c d, 8, 9, 11, 12, 13 15 e g
• 3.1 - 3.2 Quiz on 28 Oct.
• 3.2 1, 2 b c d, 3 b c d, 5 a c e g h i, 7 d, 8 c d, 9 a, 10, 11, 15, 16, 17, 18
• 3.3 2 c d e f, 3, 4, 5, 6 a b c, 7, 8 b, 9, 11, 14
• 3.1 - 3.3 marked exercises due Tue 01 Nov (27 exercises + 7 bonus)
  Please note exercises 4 -- 11 of section 3.3 are being collected in the NEXT homework.
  
• 3.4 1 b d e, 2 c d, 3 a, 4, 5, 6, 7, 9, 11a, 12b, 13, 15 b, 16 b, 17, 18, 19
• 3.3 - 3.4 marked exercises due Fri 11 Nov (20 exercises + 2 bonus)
  Please note exercises 4 -- 11 from section 3.3 are being collected in THIS homework.
• 3.5 1, 2 a b c e, 3 b, 4, 5, 6 c d, 7b, 8 b, 9, 10 b, 11, 12, 13, 14
  
  Supplementary Reading for Chapter 3
  1. Introduction to Real Analysis, by Bartle & Sherbert as referenced in the Ch 1 suggested reading. (see Chapter 1 for algebra of sets and Chapter 2 for order properties of R).
  2. Abstract Algebra: An Introduction, by Hungerford as referenced in the Ch 1 suggested reading. (see Chapter 2 for congruence in Z and the Appendices for a concise discussion on equivalence relations).
  3. Introduction to Graph Theory, by Richard Trudeau.
  
  
• 4.1 1, 2, 3, 4 e, 5 b c, 6 a c, 7, 8 b c, 9, 10 b, 11 c d, 15, 16 b d, 17 a d, 18 a b, 19
• 4.2 1 f h j, 2 f h j, 4 a b, 5 b e f h, 6 7, 8, 9 b, 10, 13, 14 b c d, 15, 16 d, 17, 18, 19
• 3.5 - 4.2 marked exercises will not be collected. (use for Exam 2 preparation)
• 4.3 1, 2, 3, 4, 5, 6, 8 b c d, 9 a b, 10, 11 b c, 12 a c, 13, 14 e f i
• 4.4 1 b d, 2 b d e, 3 a c, 4, 5, 7 a c, 8, 9 a c e f l
• 4.5 2 a b c d, 4 a,c, 5, 6, 8 c d, 9, 10 b c e f, 11 c, 12, 13, 15 a
• 4.6 1 b e, 2, 3 b d h j l n, 4, 5 d e f k, 6 e f, 7, 8, 9, 10
• 4.3 - 4.6 marked exercises due Fri 09 Dec (25 exercises + 4 bonus) Solutions
  
  Supplementary Reading for Chapter 4
  1. Introduction to Real Analysis, by Bartle & Sherbert as referenced in the Ch 1 suggested reading. Has a thorough treatment of sequences.
  2. Topolgy, by James Munrkes. The first chapter deals with almost everything we have covered in the course, with a nice section on functions, relevant to our discussion in sections 4.3, 4.4 and 4.5. There is also an appendix to this chapter on well-ordering worth reading.
  
  
• Professor Wilson's Math 300 Review Session 14:00-17:00, Sun 13 Nov, Hill 114.
  

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  Exam #2 covering Sections 2.5 -- 4.2 on Fri 18 Nov (in class). Sample of a midterm I gave the last time I taught Math 300 with solutions. Our exam solutions are here.

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• 5.1
• 5.2
• 5.3
• 5.4 optional reading
• 5.5 optional reading
• 5.1 - 5.3 exercises will not be collected. (use for Final Exam preparation)
  
  Supplementary Reading for Chapter 5
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  2.
  3.
  4.
  5.
  
  

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  Final Exam is on 22 Dec in TBA, 8:00 - 11:00 AM.

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