Mindanao State University
COLLEGE OF NATURAL SCIENCES AND MATHEMATICS
MATHEMATICS DEPARTMENT
Marawi City
Course Syllabus in MATH 111
1st Semester, AY 2018-2019
A. COURSE INFORMATION
Course Code Math 111
Course Title Introductory Analysis
Course Credit Units (hrs/wk & hrs/sem) 3 units (3 hrs/wk & 54 hrs/sem)
Course Description This course is designed as a transitional material between intuition-based calculus and rigorous analysis.
Course Objectives At the end of this course, the students are expected to:
1. become acquainted with the basic tools in calculus for higher level of mathematical analysis
2. solidify their understanding in analysis for rigorous proving.””
Prerequisite(s) Math 101, Math 71
Textbooks & References Textbook : Introduction to Real Analysis by Robert G. Bartle and Donald R. Bartle
References : Real Analysis by H.L. Royden
Principle of Mathematical Analysis by Walter Rudin
The Elements of Real Analysis by Robert G. Bartle
Course Requirements/Grading System First Major Exam : 25%
Second Major Exam: 25%
Third Major Exam : 25%
Problem Sets : 25%
--------
100% Passing cut-off rate : 50%
Classroom Policies 1. Attendance is a must. Incurring of three (3) consecutive unexcused absences shall automatically be dropped from the roll.
Accumulated absences shall be limited to 20% of the total number of class hours.
2. Problem sets and assignments must be submitted on or before the set deadline.
3. Cheating is strictly prohibited.
4. Use of mobile phones during class is strictly prohibited.
5. Special examinations are given to those students who have not taken major exams but have valid reason.
Others Instructor:
Class Schedule:
Room:
Consultation Hours:
B. LEARNING PLAN
Learning Outcomes Topics Time Methods/Learning Resources Assessment
Frame Activities
Chapter I. Review on Set Theory 1.1. The Algebra of Sets
1. Recall sets operations. a. Equality
2. Define functions. b. Set Operations
3. Identify image and domain of functions. 1.2. Functions
4. Perform operations of functions. a. Definition of a function
5. Distinguish different types of functions. b. Restriction and Extension Oral recitations
6. Apply Principle of Mathematical c. Composition of functions Board works
Induction in proving general statements d. Injective and Inverse Textbooks Assignments
involving N e. Surjective an Bijective 9 hrs Lecture-Discussion Lecture Notes Problem Sets
7. Distinguish finite from infinite sets. 1.3. Mathematical Induction Visual aids
8. Discuss the uncountability of R and a. Well-Ordering Property of N
the unit interval I. b. PMI
c. Principle of Strong Induction
1.4. Infinite Sets
a. Finite and Infinite Sets
b. The Uncountability of R and I
Chapter II. The Real Numbers 2.1. The Algebraic Properties of R
1. Identify the different field properties of R. 2.2. The Order Properties of R
2. Illustrate order properties of R in a real 2.3. Absolute Value Oral recitations
number line. 2.4. The Completeness Assignments
3. Apply order properties of R in solving Property of R Textbooks Problem Sets
linear inequalities a. The Supremum Property of R 15 hrs Lecture-Discussion Lecture Notes
4. Determine the infima and suprema of sets. b. The Archimedean Property Visual aids
c. The Density Theorem
5. Demonstrate the uncountability of R and I. 2.5. Intervals, Cluster Points First Major Exam (Chap I and II)
6. Characterize open and closed sets in and Decimals
terms of neighborh 2.6. Open and Closed Sets in R
Chapter III. Sequences 3.1. Sequences and Their Limits
1. Define sequences and limits of sequences.
2. Evaluate limits of sequences using 3.2. Limit Theorems
definitions Oral recitations
3.3. Monotone Sequences Assignments
3. Compute limits using theorems on limits. Textbooks Problem Sets
4. Prove important theorems on sequences 3.4. Subsequences and the 18 hrs Lecture-Discussion Lecture Note
and limits. Bolzano-Weierstrass Theorem Class Reporting Visual aids
5. Establish convergence or divergence of
sequences. 3.5. The Cauchy Criterion Second Major Exam ( Chap III)
6. Characterize bounded and unbounded
sequences. 3.6. Properly Divergent Sequences
Chapter IV. Limits and Continuity 4.1. Limits of Functions
1. Define limits of functions. Textbooks
2. Interpret the limit of function 4.2. Limit Theorems 12 hrs Lecture-Discussion Lecture Notes
geometrically. Class Reporting Visual aids Oral recitations
3. Establish limits of functions using the 4.3. Some Extensions of the Assignments
ε −δ criterion. Limit Concept Problem Sets
4. Evaluate limits of function using theorem
on limits of functions. 4.4. Continuous Functions Third Major Exam ( Chap IV)
5. Define continuity of functions.
6. Characterize continuity of functions
using sequences.
Prepared by: Recommending Approval: Approved:
__________________________________ ____________________________________ ___________________________________
Nestor G. Acala, PhD Raylee J. Gasparin, PhD Henry P. Aringa, PhD
(Course Coordinator) (Chairperson) (Dean)
