MATH 2710 – Transition to Advanced Mathematics – Fall 2024

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Description:

Basic concepts, principles, and techniques of mathematical proof common to higher mathematics. Logic, set theory, counting principles, mathematical induction, relations, functions. Concepts from abstract algebra and analysis. Students intending to major in mathematics should ordinarily take this course during the third or fourth semester. Students wishing to use MATH 2710 or 2710W as a prerequisite for later MATH courses need to earn a “C” or better.

Meets: Tuesdays and Thursdays, 9:30-10:45am, at MONT 227

 

Instructor: Álvaro Lozano-Robledo

Alvaro Lozano-Robledo in action (Shawn Kornegay/UConn Photo)

 

Website: http://alozano.clas.uconn.edu/
Office Hours: Mondays 1-2pm (online – find link in HuskyCT or email), Tuesdays 3-4pm (in-person at MONT 233), or by appointment.
Office: Monteith 233.

I’m a Professor of Mathematics. The focus of my research is in number theory, and more concretely in the study of elliptic curves, and other abelian varieties. 

 

Resources:

I will be following “Book of Proof” by Richard Hammack. The book is available for free (in PDF format) in the author’s website, and can also be purchased in physical form online (e.g., Amazon).

Homework problems and solutions:

Most of what you learn in this course will be the result of working exercises that are designed to reinforce key concepts, develop skills, and test your understanding of the material. There will be textbook exercises due at the end of every other week on lecture material. Some of the exercises are straightforward, others are very complex.

Late homework will not be accepted. Although it should be done daily, it will only be collected once every other week, in class or by email (MONT 233) *before* 10:45AM. Homework will only be graded on completion.

You are encouraged to talk with your classmates about the homework. If you have difficulties, do not waste time — get help! Please come to office hours!

Homework assignments. The problems below are suggested exercises. The problems in bold face will be collected on the indicated date.

  • Homework 1 (due Thursday, Sep. 12th, by 1:45pm)
    • Chapter 1:
      • Section 1.1: 14, 16, 20, 26, 32, 36, 42, 50
      • Section 1.2: 2(b,g), 8, 14, 16
      • Section 1.3: 2, 6, 10, 12
      • Section 1.4: 4, 10, 14, 18
      • Section 1.5: 2(a,b,c), 4(a,b,c), 6, 8
      • Section 1.6: 2(a,b,c)
      • Section 1.7: 6, 8
      • Section 1.8: 4, 6
    • Chapter 2:
      • Section 2.1: 2, 4, 6, 10
      • Section 2.2: 8
      • Section 2.3: 2, 4, 8, 10
      • Section 2.4: 2, 4
      • Section 2.5: 2, 4, 6, 8
      • Section 2.6: 2, 4, 10
      • Section 2.7: 2, 4, 8
      • Section 2.9: 4, 6, 10
      • Section 2.10: 2, 4, 6, 10
  • Homework 2 (due Tuesday, Sep. 24th, by 1:45pm)
    • Chapter 4: 2, 6, 12, 14, 18, 20, 22, 24 (suggested: all other exercises in Ch. 4)
    • Chapter 5: 2, 4, 6, 12, 16, 20, 22, 30 (suggested: all other exercises in Ch. 5)
  • Homework 3 (due Tuesday, Oct. 15th, by 1:45pm)
    • Chapter 6: 2, 4, 8, 16, 18, 20, 24  (suggested: all other exercises in Ch. 6)
    • Chapter 7: 2, 6, 8, 16, 22, 30, 34 (suggested: all other exercises in Ch. 7)
  • Homework 4 (due Tuesday, October 29th , by 1:45pm)
    • Chapter 8: 4, 6, 10, 22, 24, 28 (suggested: all other exercises in Ch. 8)
    • Chapter 9: 2, 6, 12, 20, 22, 30 (suggested: all other exercises in Ch. 9)
  • Homework 5 (due Thursday, November 14th, by 1:45pm)
    • Chapter 10: 2, 4, 8, 10, 16, 18, 24 (suggested: the rest)
    • Chapter 3: 2.2, 3.4, 4.16, 5.10, 6.5 and 6.6, 7.8 (suggested: all others)
  • Homework 6 (due Tuesday, December 3rd, by 1:45pm)
    • Chapter 11: 1.2, 1.6, 2.4, 2.16, 3.8, 5.2.
    • Chapter 12: 1.2, 2.12, 4.4, 4.8, 5.4, 6.2, 6.6.
    • Chapter 13: 2.2, 2.6, 3.2.
    • Chapter 14: 1.2, 1.6.

 

Information about exams and grading for your class:

Your grade in the course will be determined by your performance on the two midterm exams, a final exam, and your lecture grade. The lecture grade consists primarily of homework and class participation. Your entire grade is out of 550 points (see below):

Here you will find information about midterms and exams.

  • FIRST EXAM: Thursday, September 26th, in-class.
    • Covers Chapters 1, 2, 4, 5 (set theory, logic, direct proofs and contrapositive proofs).
  • SECOND EXAM: Thursday, October 31st, in-class.
    • Covers Chapters 6, 7, 8, 9 (contradiction, proving conditional statements, proofs involving sets, disproof)
  • FINAL EXAM: TBA. (Check the final schedule at the registrar’s website.)

The final exam will cover material from the entire course, but there will be an emphasis on material covered after the second prelim. No calculators are allowed on exams.

Grade: The grading will be based on Prelim 1 (100 points), Prelim 2 (125 points), the final exam (175 points) and a lecture grade (150 points). The lecture grade will be based on homework and class participation.

WARNINGS:

  1. If you cannot take an exam at the scheduled time, you MUST let your instructor know BEFORE the exam; you will almost certainly get an ’F’ on an exam if you miss it for any reason and then try to explain later.
  2. Incompletes will be given only under exceptional circumstances and then only to students who have a passing grade on a substantial part of the course. Do not expect to be granted an incomplete simply because you have fallen behind in the course. 

Schedule:

  • Week 1. Sets
  • Week 2. Logic
  • Week 3. Direct proof
  • Week 4. Contrapositive proof
  • Week 5. Exam 1. Proof by contradiction
  • Week 6. Proving non-conditional statements
  • Week 7. Proofs involving sets
  • Week 8. Disproof
  • Week 9. Mathematical induction
  • Week 10. Exam 2. Counting
  • Week 11. Relations
  • Week 12. Functions
  • Week 13. Proofs in Calculus
  • Week 14. Cardinality of sets.

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