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Syllabus ( MATH 303 )


   Basic information
Course title: Real Analysis I
Course code: MATH 303
Lecturer: Prof. Dr. Emil NOVRUZ
ECTS credits: 7
GTU credits: 3 (3+0+0)
Year, Semester: 3, Fall
Level of course: First Cycle (Undergraduate)
Type of course: Compulsory
Language of instruction: English
Mode of delivery: Face to face
Pre- and co-requisites: Math 111
Professional practice: No
Purpose of the course: To study Lebesgue and Measure Integral.
   Learning outcomes Up

Upon successful completion of this course, students will be able to:

  1. Explain measurable sets and Lebesgue measure.

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.

    Method of assessment

    1. Written exam
  2. Explain the Lebesque integration.

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.

    Method of assessment

    1. Written exam
  3. Distinguish the relationship between Lebesgue and Riemann integral .

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Exhibiting professional and ethical responsibility.

    Method of assessment

    1. Homework assignment
   Contents Up
Week 1: Real number sets
Week 2: Outer measure and its properties,algebra of measurable sets
Week 3: Lebesque Measure, Borel sets
Week 4: Measurable functions and its properties
Week 5: Egoroff and Lusin theorems
Week 6: Convergence in terms of measure, The Lebesque integral and properties
Week 7: MIDTERM EXAM 1 and solutions
Week 8: Passage to the limit in the integral
Week 9: Lebesque’s, Fatou’s and Levi’s theorems
Week 10: Comparison of the Lebesque and Riemann integrals
Week 11: Product measures, Fubini’s theorem
Week 12: MIDTERM EXAM 2 and solutions
Week 13: Monotone functions, bounded variation and absolutely continuous functions
Week 14: Absolutely continuity of Lebesque integral, construction of a function depending on its derivative
Week 15*: -
Week 16*: Final exam
Textbooks and materials: H.L. Royden, “Real analysis”; “ Introductory real analysis” A. N. Kolmogorov, S. V. Fomin translated and edited by Richard A. Silverman.
Recommended readings: “Elements of real analysis” David A. Sprecher.; “Introduction to real analysis” , Robert G. Bartle, Donald R. Sherbert.
  * Between 15th and 16th weeks is there a free week for students to prepare for final exam.
Assessment Up
Method of assessment Week number Weight (%)
Mid-terms: 7, 12 25
Other in-term studies: 13 25
Project: 0
Homework: 3,6,9 10
Quiz: 0
Final exam: 16 40
  Total weight:
(%)
   Workload Up
Activity Duration (Hours per week) Total number of weeks Total hours in term
Courses (Face-to-face teaching): 3 14
Own studies outside class: 5 14
Practice, Recitation: 0 0
Homework: 5 3
Term project: 0 0
Term project presentation: 0 0
Quiz: 0 0
Own study for mid-term exam: 12 2
Mid-term: 4 2
Personal studies for final exam: 12 1
Final exam: 2 1
    Total workload:
    Total ECTS credits:
*
  * ECTS credit is calculated by dividing total workload by 25.
(1 ECTS = 25 work hours)
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