MM303 : Real Analysis 1

Department

Department of Mathematics

Academic Program

Bachelor in mathematics

Type

Compulsory

Credits

03

Prerequisite

MM211MM213

Overview

This course introduces the student to the basic concepts of the real number line properties of addition and multiplication operations in real numbers and the relationship of ordering real numbers with proof. It also deals with mathematical deduction - the absolute value of the real number and the solution of its inequalities after studying the properties of the absolute value - sequences of real numbers, their definition, types and convergence - sequences Finite - the Cauchy sequence - the relationship of the convergent sequence with the Cauchy sequence - the smallest upper term - the largest lower term - the Archimedes property - theories on the convergence of sequences – exercises. This course aims to develop the student's ability to determine Euclidean non-dimensional space, topology on space Rn, sequences and series in space Rn, limits and continuity.

Intended learning outcomes

By the end of the course, the student should be able to :

  1. Recognize the non-dimensional space, closed and open groups, and accumulation points for the group.
  2. Distinguish series and sequences and methods of finding limits and their convergence.
  3. It explains the end and continuity of functions and their relationship to compactness and interdependence.
  4. Explain ways to find the limits of functions.
  5. Determine the regular continuity and derivability.
  6. Prove some theories and theorems related to open groups enclosed.
  7. compare infinite series and sequences and methods of showing their convergence.
  8. Connect compact groups and interdependent groups.
  9. The student should explain the existence of the limit, the continuity, and the derivability of functions.
  10. Infer the end and continuity of functions.
  11. Solve a number of exercises and problems with more than one idea of open and closed groups.
  12. Use methods to find the limit and convergence of infinite series and sequences
  13. Apply theories related to compact and interdependent groups
  14. It gives solutions to new and different problems to find the limits of functions
  15. Use some ideas to prove and solve continuity issues

Teaching and learning methods

  1. Theoretical lectures
  2. Discussion and dialogue
  3. Brain storming
  4. Using mathematical proof methods
  5. Exercises, trainings and multi-idea problem-solving

Methods of assessments

  1. A written exam (essay + objective) = 25 marks, or its assessment is left to the course instructor.
  2. Short tests (written or oral), demonstration tasks, applications, exercises, and presentation = 15 marks, or the assessment is left to the course instructor.
  3. Written final exam (essay + objective) = 60 marks

Course content

the week

Scientific subject

The number of hours

a lecture

exercises

1

Euclidean space non-dimensional

3

2

1

2

Open and closed groups

3

2

1

3

Accumulation point, group closure and unit

3

2

1

4

Sequences and series in non-dimensional space

3

2

1

5

A first midterm exam

5-6

Absolute convergence

4

3

1

7

Series with positive terms

3

2

1

8

Metric spaces

3

2

1

9

compact groups

3

2

1

10

A second midterm exam

10

connected groups

1

1

-

11

functions ends

3

2

1

12

Continuous functions

3

2

1

13

properties of continuous functions

3

2

1

14

regular continuity

3

2

1

15-16

A final exam

the total

42

References

References address

publisher

Release

Author

real analysis

International House for Publishing and Distribution

the second

Dr . Ramadan Mohamed Juhayma

Mathematical analysis

University of Tripoli Publications

The first

Translated by Ali Mohamed Ibrahim

Arabic language 1 (AR103)
Linear Algebra 1 (MM105)
Planar and Analytical Geometry (MM103)
Quranic Studies 1 (AR101)
computer 1 (CS100)
General Mathematics 1 (MM101)
General English1 (EN100)
Fundamentals of Education (EPSY101)
General Psychology (EPSY 100)
Introduction to Statistics (ST101)
Quranic studies2 (AR102)
Aerospace Engineering (MM114)
General Mathematics 2 (MM102)
Linear Algebra (2) (MM215)
Developmental Psychology (EPSY 203)
General Teaching Methods (EPSY 201)
General English2 (EN101)
Computer 2 (CS101)
Introduction to the science of Probabilities (ST102)
Arabic language 2 (AR104)
Basics Of Curriculums (EPSY 202)
Mathematical Logic (MM317)
Educational Psychology (EPSY 200)
Arabic language 3 (AR105)
Ordinary Differential Equations 1 (MM202)
Static (MM206)
General Mathematics3 (MM211)
Ordinary Differential Equations 2 (MM311)
Vector analysis (MM214)
Mathematical statistics (ST202)
Set Theory (MM213)
Arabic language 4 (AR106)
Research Methods (EPSY301)
Measurements and Evaluation (EPSY 302)
Methods of teaching mathematics (MM208)
Teaching learning Aids (EPSY 303)
Word processing (CS 202)
Psychological Health (EPSY 401)
School mathematics 1 (MM309)
Complex Analysis 1 (MM305)
Real Analysis 1 (MM303)
Dynamics (MM207)
Abstract Algebra 1 (MM302)
Complex Analysis 2 (MM306)
School mathematics2 (MM310)
Real Analysis 2 (MM304)
Abstract Algebra 2 (MM403)
Numerical Analysis (MM308)
measurement theory (MM410E)
Integral equations (MM409E)
Operations Research (MM408E)
History of Mathematics (MM407E)
Functional Analysis (MM406E)
linear programming (MM405E)
Partial Differential Equations (MM401)
Teaching applications (MM400)
Graduation project (MM404)
Teaching Practice (EPSY 402)