Module Handbook-Mathematics-Universitas Brawijaya
Module Handbook
Module Name: Introduction to Real Analysis I
Module Level: Bachelor
Abbreviation, if Applicable:
MAM61204 Sub-Heading, if
Applicable:
- Courses included in the module, if applicable
Introduction to Real Analysis I Semester/term: 5th/ 3rd year
Module Coordinator(s): Chair of the Lab. Analysis Lectures(s) Drs. M. Muslikh, M.Si., Ph.D
Corina Karim, S.Si., M.Si., Ph.D Sa’adatul Fitri, S.Si., M.Sc
Language Bahasa Indonesia
Classification within the curriculum
Compulsory Course Teaching format / class
hours per week during semester:
200 minutes lectures per week.
Workload: Total workload is 6 ECTS, which consists of 3.33 hours lectures, 4 hours structured activities, 4 hours independent learning, 16 week per semester, and a total 181.33 hours per semester including mid exam and final exam.
Credit Points: 4
Requirements according to the examination regulations:
Students have attendance at least 80% on Introduction to Real Analysis I class and registered as examinees in the academic information system.
Recommended prerequisties
Students have taken Calculus III course (MAM61202) and have an examination card where the course is stated on
Module
objectives/intended learning outcomes
After completing this course the student should have
CLO 1 : ability to understand how real number systems constructed by rasional number using ordered field structured and use the properties.
CLO 2 : ability to determine main elements on metric space.
CLO 3 : ability to prove convergent and divergent series, use properties of series limit, inferior limit and superior series number.
CLO 4 : ability to understand limit functions and general continuous functions for solving problems or proving theorems.
CLO 5 : ability to understand relationship between continuity of functions with compactness and connected of its domain.
Module Handbook-Mathematics-Universitas Brawijaya
Content: Topics:
1. Real Numbers system ℝ: properties of real numbers system, order relation,absolute value.
2. Sequence of real numbers: convergence, Cauchy criteria, relation between Cauchy criteria and convergence of sequences.
3. Limit of functions: definition and properties of limit.
4. Continuity: definition, properties of continuous functions, uniformly continuous.
Soft Skill Attribute Discipline, honesty, cooperation and communication Study / exam
achievements:
The final mark will be weighted as follows:
No. Assessment methods (component, activities). Weight
1. Assignment 20 %
2. Quiz 20 %
3. Mid examination 30 %
4. Final examination 30 %
Final grades is defined as follow: A : 80 < Final Mark ≤ 100 B+ : 75 < Final Mark ≤ 80
B : 69 < Final Mark ≤ 75
C+ : 60 < Final Mark ≤ 69
C : 55 < Final Mark ≤ 60
D+ : 50 < Final Mark ≤ 55
D : 44 < Final Mark ≤ 50
E : 0 ≤ Final Mark ≤ 44
Forms of Media Slides and LCD projectors, laptop/ computer, whiteboards.
Learning Methods Lecture
Literature 1. Muslikh, M., 2012, Analisis Real, UB.Press , Indonesia 2. Soemantri, R.,1990, Analisis Real I, PT. Karanika, Jakarta
3. Rudin, W., 1976, Principles of Mathematical Analysis 3rd Edition, McGraw-Hill, New York, Inc.
4. Apostol, T.M., 1974, Mathematical Analysis, 2nd Edition, Addison Wesley Publish.Com.
5. Goldberg, R., 1976, Methods of Real Analysis 2nd Edition, John- Willey
Notes:
