SYLLABUS

Bridge Course in Mathematics (BC-102(N2))

Max. Marks 100 Internal Assessment 40

External Assessment 60

Instruction for paper setterThe question paper will consist of two sections A and B. Sections B will have Six questions and will carry 10 marks each. Section A will have 10 short answer type questions, which will cover the entire syllabus uniformly and will carry 20 marks in all.

Instructions for CandidatesCandidates are required to attempt four questions from section B and the entire section A.Use of non-programmable scientific calculator is allowed.

Set relations and functions: elements of a set, methods of describing a set, types of set, Venn diagram, operations on sets, union, intersection and difference of set, Duality, partioning of a set, trigonometric functions.

Binomial theorem and principle of mathematics induction

Introduction to matrix, properties of matrix; evaluation of determinant, minor and cofactors and properties of determinant

Statistics: introduction to statistics, collection, and tabulation of data, mean, median and mode.

Reference:

Refresher Course On Mathematics Vol: 2--- Manjit Singh

ABC Of Mathematics J.P Mahendru

Note: This course is compulsory for all the students.

COURSE MODULE

COURSE NAME: BRIDGE COURSE IN MATHEMATICSCLASS : BCA-ICOURSE CODE : BC-102

COURSE INSTRUCTOR: Mr. SWAPAN CHANANA, Mr. RAHUL ARORA Ms Prabhjot

COURSE OBJECTIVES:

‘Bridge Course in Mathematics’ is a course which is especially incorporated with a view to create a bridge between the elementary mathematics that you have studied till 10th standard, and all that you will require for computer courses that you will study in BCA.

‘Statistics’ is a very important branch of mathematics which is closely connected with the industry. Mean, Median, Mode & other measures of Central Tendency are basic to the processing of any kind of data, to convert it into useful information which is of strategic importance to any company or business house.

This course will teach you the fundamentals that are essential for other courses like Digital Circuit & Logic Design (Logic Gates, Functions & Relations), Computer Oriented Mathematics & Computer System Architecture (Binary Number System, Boolean Algebra).

So, ‘Bridge Course in Mathematics’ is your first step to becoming Computer Professionals.

PRESENTATION:

There will be one presentation for the subject. The students will be divided into different groups. Each group will work upon a topic and present it. The schedule of the same will be intimated to you.

DISTRIBUTION OF MARKS:

Bridge Course in Mathematics carries 100 marks. Out of these, the students will be tested externally for 60 marks, and internally for 40 marks.The external exam will carry 60 marks, which will be in December.The internal exam (MST - Mid Semester Test) will be in October.The division of 40 marks for the internal assessment is as follows :

MST - 15 marksPresentation - 10 marksAssignments - 5 marksClass Tests - 10 marks

PUNJAB COLLEGE OF TECHNICAL EDUCATION (PCTE)

COURSE PLAN Aug-Dec, 2010

SUB NAME : BRIDGE COURSE IN MATHS SUB CODE : BC – 102SUB TEACHERS : Mr. SWAPAN CHANANA Mr.RAHUL ARORA

No. of lectures : 54

No. of Tests : 2 No. of Assignments : 2Lecture Number

Topics Assign Test

1 Chapter: Matrix Algebra• Introduction & definition of

matrices• Types of Matrices

•

2 Matrix Operations• Addition• Difference• Multiplication

3 • Positive Integral powers of matrices• Problems on multiplication of

matrices4 Determinants

• Transpose, Symmetric and skew symmetric matrices

• Determinants of a square matrix

•

5 • Minors and Cofactors• Sarus Rule• Problems on Sarus Rule

6 • Tutorial

7-8 • Cramers Rule

8-11 • Properties of Determinants• Related Problems

12-13 • Related Problems contd…

14-15 Chapter: Binomial Theorem• Introduction• Pascal’s Triangle• Binomial Theorem

16-18 • General Term• Middle Terms• Related Problems

19-20 • Particular Terms• Examples

21-22 • Properties of Binomial Coefficients

23 • Binomial Theorem for any Index

24 • Related Problems

25 • Applications of Binomial Theorem

26-27 Chapter: Sets, Relations and Functions• Introduction• Definition of a set• Representation of a set• Types of sets

•

28-30 Venn Diagrams• Introduction• Operations on Sets

Union Intersection Disjoint Difference

31 Statement problems

32 Laws of Algebra of Sets• DeMorgan’s Laws• Related Proofs

33-34 • De-Morgan’s Law of Difference of Sets

35 Duality• Related ProblemsRelations• Ordered Pairs • Cartesian Product of Sets

36 • Definition of a Relation• Types of Relations

37-38 • Domain & Range

39 Functions or Mappings• Definition• Types of Functions

40 • Composite Functions• Problems

41 • Functions Contd…

42 Chapter: Mathematical Induction• Introduction• Statements• Mathematical Statements• Examples

•

43 Principle of Mathematical Induction• Series Problems

44 • Problems involving inequalities

45 • Exponential Problems

46 • Statement Problems

47 Chapter: Trigonometric Functions• Introduction• T-Ratios or Functions

48-50 • T-Identities

51 • Problems Based on T-Identities

52-53 • Proving results involving T-Ratios

54 • Signs of T-Ratios• Values of T-Ratios• Related Problems

55 • T-Ratios of Allied Angles

56 • T-Ratios of Sum or Difference of 2 angles

• Examples57-58 Chapter: Statistics

• Introduction• Definition of Statistics• Statistical Methods• Collection of Data• Tabulation of data : Frequency

Distributions59 Measures of Central Tendency

• IntroductionArithmetic Mean

Individual Observations Discrete Frequency

Distribution Continuous Frequency

Distribution60 • Properties of Arithmetic Mean

• Related Examples• Merits and Demerits

48 • Tutorial

49 Median• Individual Series• Discrete Frequency Distribution• Continuous Frequency Distribution

50 • Related Problems• Mathematical Property of Median• Merits and Demerits of median

51 Mode• Individual Series• Discrete Series• Grouping Method• Continuous Series

52 • Mode greater than the Upper Limit of Modal Class

• Bi-Modal Distribution• Mode less than the Lower Limit of

Modal Class• Merits and Demerits

53 Revision of Syllabus

54 Full Test