MAA 4102 Intro Real Analysis 1 Period 5 (Fall 2025)

  • Instructor: Sergei S. Pilyugin
  • Course web page: https://people.clas.ufl.edu/pilyugin/courses/maa4102_f2025_p5/
  • Announcements: Lectures will be delivered live in LIT 0219 (this class has no online component). Quizzes and midterms will be given in class. All test scores will be posted in canvas.
  • Homeworks: List of HW problems.
  • Prerequisites: MAC 2313 (Calculus 3).
  • Time and Room: MWF 5 (11:45 a.m. – 12:35 p.m.) in LIT 0219.
  • Literature: M. Spivak, Calculus (4th ed.), Publish or Perish Inc. (ISBN: 9780914098911).
  • Critical dates: 08/21 classes begin, 12/03 classes end. Midterms: M1 – 09/26, M2 – 10/24, M3 – 11/19. Quizzes: Q1 – 09/05, Q2 – 09/19, Q3 – 10/10, Q4 – 11/12, Q5 – 12/01.
  • Holidays: 09/01 Labor Day, 10/17 Homecoming, 11/11 Veterans Day, 11/24–29 Thanksgiving break.
  • Office Hours: MWF 4 (10:40 a.m.-11:30 a.m.) in LIT 0458, or in zoom (see info in canvas) by appointment. Please, use e-mail: pilyugin@ufl.edu for general inquiries or canvas messaging tool for all private communication including all questions regarding scores/grades. For more details, see my schedule.
  • Description and Objectives of the Course:

    • What is the difference between the real analysis and the calculus courses that you have taken previosuly? In real analysis, we revisit familiar concepts (real numbers, sequences, functions, limits, continuity, differentiation and integration, etc), but the material is treated in a more accurate and rigorous way. So, the main difference is that we have PROOFS here.

    Tentative Weekly Schedule:

    W1: Properties of numbers, basic inequalities; 
    W2-3: Various number systems, intro to proofs, mathematical induction; 
    W4-5: Functions and graphs;
    W6-7: Limits and continuity;
    W8: Properties of continuous functions;
    W9: Supremum and infimum;
    W10: Uniform continuity;
    W11-12: Derivatives and differentiation techniques;
    W13-14: Mean value theorems, L’Hopital’s rule, inverse functions, convexity/concavity.

  • Grading System:
    3 midterms (20% each, in class); 5 quizzes (10% each, best 4 count, in class) based on homework assignments. There will be no final exam. The resulting score determines the letter grade according to the following table

    Letter Grade
    A
    A-
    B+
    B
    B-
    C+
    C
    C−
    D+
    D
    Score ≥ 92 ≥ 89 ≥ 85 ≥ 81 ≥ 77 ≥ 72 ≥ 67 ≥ 62 ≥ 56 ≥ 50
  • Closed-book policy: No use of calculators, or books will be allowed during in-class quizzes.
  • Grading disputes: Any issues or questions about the grading of exams must be brought to the instructor’s attention within one week after the exams are returned to the class.
  • Excused absences: In certain circumstances, a student will be able to make up a missed quiz. These circumstances could include medical situations, family emergencies, travel for University activities (eg. band, debating club, etc), and religious observances. In these cases the student must inform the instructor before or within one week after the missed work and provide written documentation. All make ups must be taken no later than the last day of classes.
  • Other UF policies: This course complies with all UF academic policies. For information on those polices and for resources for students, please use this link.