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# Course module maths

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### Course module maths

1. 1. SYLLABUS Bridge Course in Mathematics (BC-102(N2)) Max. Marks 100 Internal Assessment 40 External Assessment 60 Instruction for paper setter The 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 Candidates Candidates 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.
2. 2. COURSE MODULE COURSE NAME: BRIDGE COURSE IN MATHEMATICS CLASS : BCA-I COURSE 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 :
3. 3. MST - 15 marks Presentation - 10 marks Assignments - 5 marks Class Tests - 10 marks PUNJAB COLLEGE OF TECHNICAL EDUCATION (PCTE) COURSE PLAN Aug-Dec, 2010 SUB NAME : BRIDGE COURSE IN MATHS SUB CODE : BC – 102 SUB TEACHERS : Mr. SWAPAN No. of lectures : 54 CHANANA Mr.RAHUL ARORA No. of Tests : 2 No. of Assignments : 2 Lecture Topics Assign Test Number 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 matrices 4 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
4. 4. 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 Problems Relations • 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…
5. 5. 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 • Examples 57-58 Chapter: Statistics • Introduction • Definition of Statistics • Statistical Methods • Collection of Data • Tabulation of data : Frequency Distributions 59 Measures of Central Tendency • Introduction Arithmetic Mean  Individual Observations  Discrete Frequency Distribution  Continuous Frequency Distribution 60 • Properties of Arithmetic Mean • Related Examples • Merits and Demerits
6. 6. 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