MA3522

MA3522 Analysis

Part I

Course Duration: One semester
Credit Units: 3
Level: B3
Medium of Instruction: English
Prerequisites: MA2502 or MA2508
Precursors: Nil
Equivalent Courses: Nil
Exclusive Courses: MA2501

Part II

Course Aims
This course gives rigorous analysis on the real line and higher dimensional Euclidean spaces. It trains students to prove mathematical theorems rigorously.

Course Intended Learning Outcomes (CILOs)
Upon successful completion of this course, students should be able to:

No.
CILOs Weighting (if applicable)
1. explain rigorously concepts of limit and continuity. 2
2. recognize basic properties of metric space. 2
3. understand the concepts of uniform continuity and uniform convergence. 2
4. the combination of CILOs 1-3. 3

Weighting scale: 1 - Least important; 2 - Important; 3 - Highly important

Teaching and Learning Activities (TLAs)
Indicative of likely activities and tasks students will undertake to learn in this course. Final details will be provided to students in their first week of attendance in this course.

TLAs
ILO No. Hours/week
Learning through teaching is primarily based on lectures. 1--4 39 hours in total
Learning through take-home assignments helps students understand basic concepts and techniques of analysis. 1--4 after-class
Learning activities in Math Help Centre provides students extra help. 1--4 after-class

Assessment Tasks/Activities
(Indicative of likely activities and tasks designed to assess how well the students achieve the CILOs. Final details will be provided to students in their first week of attendance in this course)

30% Coursework
70% Examination (Duration : 3 hours: at the end of the semester)

For a student to pass the course, at least 30% of the maximum mark for the examination must be obtained.

Assessment Tasks/Activities
ILO No. Weighting (if applicable) Remarks
Test
1--2
30% Questions are designed for the first part of the course to see how well students have learned concepts about limit, continuity and sets.
Hand-in assignments
1--4
These are skills based assessment to help students understand basic concepts and techniques of analysis.
Examination
4
70% Examination questions are designed to see how far students have achieved their intended learning outcomes. Questions will primarily be skills and understanding based to assess the student’s versatility in analysis.
Formative take-home assignments
1--4
0% The assignments provide students chances to demonstrate their achievements on analysis learned in this course.

Grading of Student Achievement: Refer to Grading of Courses in the Academic Regulations

Letter Grade
GradePoint Grade Definitions
A+
A
A- 4.3
4.0
3.7 Excellent Strong evidence of original thinking; good organization, capacity to analyze and synthesize; superior grasp of subject matter; evidence of extensive knowledge base.
B+
B
B- 3.3
3.0
2.7 Good Evidence of grasp of subject, some evidence of critical capacity and analytic ability; reasonable understanding of issues; evidence of familiarity with literature.
C+
C
C- 2.3
2.0
1.7 Adequate Student who is profiting from the university experience; understanding of the subject; ability to develop solutions to simple problems in the material.
D 1.0 Marginal Sufficient familiarity with the subject matter to enable the student to progress without repeating the course.
F 0.0 Failure Little evidence of familiarity with the subject matter; weakness in critical and analytic skills; limited, or irrelevant use of literature.

Part III

Keyword Syllabus
Limit, continuity, least upper bound axiom, open and closed sets, compactness, connectedness, differentiation, uniform convergence and generalization to higher dimensions.