MANAGEMENT MATHEMATICS I
KCA UNIVERSITY
COURSE OUTLINE:
Course Code: CMS 101
Course Title: MANAGEMENT MATHEMATICS I
Course Purpose: The course introduces the tools of obtaining, summarising, analysing
information. It introduces Set theory, functions, equations ,sequences and
mathematics of finance .
Course Objectives:
The learner will be able to;
a) Apply various techniques to deal with problems of obtaining and analysing data.
b) Identify and explain functions and inequalities.
c) Solve problems using various mathematical tools.
Course outline:
• Set theory and its applications: sets, elements of a set, Types of sets , Venn diagrams,
Basic set operations , set enumeration and applications of sets to counting problems.
• Functions , Equations, inequalities and their applications; linear functions, quadratic
functions linear equations, simultaneous equations, Quadratic equations linear
inequalities, exponential functions, logarithmic functions, and applications to sales
commissions ,demand functions, supply functions c-v-p analysis ,etc.
• Sequences and Series; arithmetic progression sequences& series, geometric progression
Sequences & series and their applications
• Mathematics of finance; time value of money, compound value, present value,
annuities and investment appraisals.
Teaching Methodology:
Lectures, tutorials , discussion and problem solving exercises.
Instructional Materials/Equipment
Class with visual aids
Course Assessment/Student Performance
Continuous Assessment: 30%
Examination: 70%
1
,(Grading as detailed under examination regulations)
Textbooks:
1. Chiang, Alpha C: Fundamental Methods of Mathematical Economics – 3rd edition,
Auckland McGraw Hill, 1984.
2. Budrick, FS; Applied Mathematics for Business, Economics, and the Social Sciences
– 4th edition, New York; McGraw Hill, 1993.
Further reading
3. Swift, Lois: Quantitative Methods for Business, Management and Finance – London
Palgrave Macmillan, 2001.
4. Oakshoft, Les: Essential Quantitative Methods for Business, Management and
Finance – 3rd ed. – Boston: McGraw Hill, 1998.
LECTURE ONE: SET THEORY
1.1 Introduction
Welcome to the first lecture in Management mathematics I. We shall learn several
techniques of solving problems encountered in business. We shall begin the study of
this unit by highlighting the meaning of management mathematics. We will further
explain terms in Set theory.
1.2 Specific objectives:
By the end of this lesson you should be able to:
i) Define Mathematics
ii) Define Management Mathematics
iii) Define the term Set
iv) State the elements of a set
v) State and explain various types of sets
1.3 Lecture Outline
1.3.1 Definition of Mathematics.
1.3.2 Definition of management mathematics and its importance in business
1.3.3 Definition of a set and elements of a set
1.3.4 Importance of sets
1.3.5 Types of sets
1.3.1 Definition of Mathematics.
2
, Mathematics is the study of quantity, structure, space, and change.
Mathematicians seek out patterns, formulate new conjectures, and establish truth
by rigorous deduction from appropriately chosen axioms and definitions.
Mathematics is used throughout the world as an essential tool in many fields,
including natural science, engineering, medicine and the social sciences
1.3.2 Definition of management mathematics and its Importance in Business
Management Mathematics is concerned with the application of mathematics and
statistics in managerial and Business decision making. Mathematical techniques
and shortcuts are a vital foundation for decisions made on the allocation of
resources, time, budgets, Sequencing of tasks, personnel assignment, contingency
planning and other managerial decisions.
In this module, more emphasis will be put on the application of Set theory,
functions, equations ,sequences and mathematics of finance .
1.3.3 Definition of a set and elements of a set
A set is a group of objects with similar characteristics eg a group of students, books in
the library, integers, degree courses etc. sets are usually denoted using capital letters eg
A,B,C,D, etc.
The objects that are in a set are referred to as its members or elements. Elements are
usually represented by small letters eg a, b, c, d, etc. Elements of a given set must be
distinguished i.e. each element is mentioned or appear only once.
But the order of mentioning the elements of a set is irrelevant eg A=[1,2,3,4]= {2,1,4,3}.
Set membership is expressed using the greek letter epsilon ,
Eg if A= [a,b,c,d,e], Then a A ’a’ is a member of set A
b A ’b’ is a member of set A
1.3.4 Importance of sets
The study of sets is popular in Business and Economic world since the basic
understanding of the concepts in sets and set algebra provides a form of logical
language through which a business analyst can communicate important concepts
and ideas. It is also used in counting problems of logical nature.
1.3.5 Types of sets
3
, a) Finite set- A set that consist of countable or specific number of elements eg
A=[2,4,6,8] is a set of four consecutive even numbers starting from 2.
b) Infinite set- A set that consist of uncountable number of elements
eg B= { All odd numbers}
c) Equal sets- Two sets A and B are said to be equal if and only if every element of
A is also an element of B and vice versa eg let A=[2,4,6,8] and B={4,2,8,6],Then
A=B
d) Null or Empty set- This is a set with no element and is denoted follows;
N={ } or N= -phi eg set of people born in the 17th century and are still alive
e) A sub-set- This is a set whose elements are also in another bigger set eg if
A={2,3,4,5,} and B={2,3,4,5,6,7} then A is a subset of B and is denoted by A B
f) Overlapping sets- Two sets are said to be overlapping if they have common
elements but they are not subsets of each other eg let A={15,20,25,30} and
B={10,15, 20} , Then A and B are overlapping since elements 15 and 20 are
common
g) Power set- This is a family of all subsets of any set
I) Eg let M= a, b, Then 2M= a, b, ( a, b ) ,
II) Let T 4,7,8, Then 2T= 4,7,8,(4,7,8),(4,7),(4,8),(7,8),
h) Disjoint sets-These are sets which do not have common element eg if A= 1,3,8
and B= {2,4,7,9}, then A and B are disjoint sets
i) Universal set- This is a set that contains all elements under consideration eg a set
of all students at KCA University. It is usually denoted by µ
j) Complement of a set- If A is a subset of the universal set, then complement of A
is the set of all elements not contained in A but are in the universal set.
Let µ ={1,2,3,4,5,6,7,8,9} and A {2,4,6,8}, Then complement of A= µ -A={1,3,5,7,9}
1.4 Activities
1.4.1 Differentiate between disjoint sets and Overlapping sets
1.4.2 How is management mathematics applied at your place of work and in
your home?
4
KCA UNIVERSITY
COURSE OUTLINE:
Course Code: CMS 101
Course Title: MANAGEMENT MATHEMATICS I
Course Purpose: The course introduces the tools of obtaining, summarising, analysing
information. It introduces Set theory, functions, equations ,sequences and
mathematics of finance .
Course Objectives:
The learner will be able to;
a) Apply various techniques to deal with problems of obtaining and analysing data.
b) Identify and explain functions and inequalities.
c) Solve problems using various mathematical tools.
Course outline:
• Set theory and its applications: sets, elements of a set, Types of sets , Venn diagrams,
Basic set operations , set enumeration and applications of sets to counting problems.
• Functions , Equations, inequalities and their applications; linear functions, quadratic
functions linear equations, simultaneous equations, Quadratic equations linear
inequalities, exponential functions, logarithmic functions, and applications to sales
commissions ,demand functions, supply functions c-v-p analysis ,etc.
• Sequences and Series; arithmetic progression sequences& series, geometric progression
Sequences & series and their applications
• Mathematics of finance; time value of money, compound value, present value,
annuities and investment appraisals.
Teaching Methodology:
Lectures, tutorials , discussion and problem solving exercises.
Instructional Materials/Equipment
Class with visual aids
Course Assessment/Student Performance
Continuous Assessment: 30%
Examination: 70%
1
,(Grading as detailed under examination regulations)
Textbooks:
1. Chiang, Alpha C: Fundamental Methods of Mathematical Economics – 3rd edition,
Auckland McGraw Hill, 1984.
2. Budrick, FS; Applied Mathematics for Business, Economics, and the Social Sciences
– 4th edition, New York; McGraw Hill, 1993.
Further reading
3. Swift, Lois: Quantitative Methods for Business, Management and Finance – London
Palgrave Macmillan, 2001.
4. Oakshoft, Les: Essential Quantitative Methods for Business, Management and
Finance – 3rd ed. – Boston: McGraw Hill, 1998.
LECTURE ONE: SET THEORY
1.1 Introduction
Welcome to the first lecture in Management mathematics I. We shall learn several
techniques of solving problems encountered in business. We shall begin the study of
this unit by highlighting the meaning of management mathematics. We will further
explain terms in Set theory.
1.2 Specific objectives:
By the end of this lesson you should be able to:
i) Define Mathematics
ii) Define Management Mathematics
iii) Define the term Set
iv) State the elements of a set
v) State and explain various types of sets
1.3 Lecture Outline
1.3.1 Definition of Mathematics.
1.3.2 Definition of management mathematics and its importance in business
1.3.3 Definition of a set and elements of a set
1.3.4 Importance of sets
1.3.5 Types of sets
1.3.1 Definition of Mathematics.
2
, Mathematics is the study of quantity, structure, space, and change.
Mathematicians seek out patterns, formulate new conjectures, and establish truth
by rigorous deduction from appropriately chosen axioms and definitions.
Mathematics is used throughout the world as an essential tool in many fields,
including natural science, engineering, medicine and the social sciences
1.3.2 Definition of management mathematics and its Importance in Business
Management Mathematics is concerned with the application of mathematics and
statistics in managerial and Business decision making. Mathematical techniques
and shortcuts are a vital foundation for decisions made on the allocation of
resources, time, budgets, Sequencing of tasks, personnel assignment, contingency
planning and other managerial decisions.
In this module, more emphasis will be put on the application of Set theory,
functions, equations ,sequences and mathematics of finance .
1.3.3 Definition of a set and elements of a set
A set is a group of objects with similar characteristics eg a group of students, books in
the library, integers, degree courses etc. sets are usually denoted using capital letters eg
A,B,C,D, etc.
The objects that are in a set are referred to as its members or elements. Elements are
usually represented by small letters eg a, b, c, d, etc. Elements of a given set must be
distinguished i.e. each element is mentioned or appear only once.
But the order of mentioning the elements of a set is irrelevant eg A=[1,2,3,4]= {2,1,4,3}.
Set membership is expressed using the greek letter epsilon ,
Eg if A= [a,b,c,d,e], Then a A ’a’ is a member of set A
b A ’b’ is a member of set A
1.3.4 Importance of sets
The study of sets is popular in Business and Economic world since the basic
understanding of the concepts in sets and set algebra provides a form of logical
language through which a business analyst can communicate important concepts
and ideas. It is also used in counting problems of logical nature.
1.3.5 Types of sets
3
, a) Finite set- A set that consist of countable or specific number of elements eg
A=[2,4,6,8] is a set of four consecutive even numbers starting from 2.
b) Infinite set- A set that consist of uncountable number of elements
eg B= { All odd numbers}
c) Equal sets- Two sets A and B are said to be equal if and only if every element of
A is also an element of B and vice versa eg let A=[2,4,6,8] and B={4,2,8,6],Then
A=B
d) Null or Empty set- This is a set with no element and is denoted follows;
N={ } or N= -phi eg set of people born in the 17th century and are still alive
e) A sub-set- This is a set whose elements are also in another bigger set eg if
A={2,3,4,5,} and B={2,3,4,5,6,7} then A is a subset of B and is denoted by A B
f) Overlapping sets- Two sets are said to be overlapping if they have common
elements but they are not subsets of each other eg let A={15,20,25,30} and
B={10,15, 20} , Then A and B are overlapping since elements 15 and 20 are
common
g) Power set- This is a family of all subsets of any set
I) Eg let M= a, b, Then 2M= a, b, ( a, b ) ,
II) Let T 4,7,8, Then 2T= 4,7,8,(4,7,8),(4,7),(4,8),(7,8),
h) Disjoint sets-These are sets which do not have common element eg if A= 1,3,8
and B= {2,4,7,9}, then A and B are disjoint sets
i) Universal set- This is a set that contains all elements under consideration eg a set
of all students at KCA University. It is usually denoted by µ
j) Complement of a set- If A is a subset of the universal set, then complement of A
is the set of all elements not contained in A but are in the universal set.
Let µ ={1,2,3,4,5,6,7,8,9} and A {2,4,6,8}, Then complement of A= µ -A={1,3,5,7,9}
1.4 Activities
1.4.1 Differentiate between disjoint sets and Overlapping sets
1.4.2 How is management mathematics applied at your place of work and in
your home?
4
