Revised Course
(WITH EFFECT FROM
THE ACADEMIC YEAR 2012-2013)
Why Revision?
There is a Rapid expansion of knowledge in subject matter areas and
improved instructional method during last decade. There are considerable
curricular revisions happening at the high school level. Application of
Mathematics and Statistics are widely used in industry and business. Keeping
this in mind, a revision of syllabus required in accordance with the growth of
subject of at the high school level and emerging needs of industry and its
application.
Objective:
The main objective of this course is to introduce mathematics and
statistics to undergraduate students of commerce, so that they can use them in
the field of commerce and industry to solve the real life problems.
Distribution of topics and lectures
Semester I
|
Course
UBCOMFSI.6
Mathematical
and
Statistical
Techniques-I
|
Topic
|
No. of lectures
|
|
Unit I
|
15
|
|
|
Unit II
|
15
|
|
|
Unit III
|
15
|
|
|
Unit IV
|
15
|
|
|
Unit V
|
15
|
|
|
Total
|
75
|
Total number of lectures 75 +Notional75=150 lectures = 3
CREDITS
Semester II
|
Course
UBCOMFSII.6
Mathematical
and
Statistical
Techniques-II
|
Topic
|
No. of lectures
|
|
Unit I
|
15
|
|
|
Unit II
|
15
|
|
|
Unit III
|
15
|
|
|
Unit IV
|
15
|
|
|
Unit V
|
15
|
|
|
Total
|
75
|
Total number of lectures 75 +Notional 75=150 lectures = 3
CREDITS
MATHEMATICAL AND
STATISTICAL TECHNIQUES
WORKLOAD:
MATHEMATICS : 2
lectures per week
STATISTICS : 3 lectures per week
TUTORIAL : 1 per
week
Tutorial batch size : 25 Students
Semester I
Course: UBCOMFSI.6
Mathematical and Statistical
Techniques-I
MATHEMATICS: (24 marks)
Unit I
Shares and Mutual Funds:
Concept of share, face value, market value, dividend, equity
shares, preferential shares, bonus shares. Simple examples.
Mutual Funds: Simple problems on calculation of Net income
after considering entry load, dividend, change in Net Asset Value(N.A.V.) and
exit load. Averaging of price under the Systematic Investment Plan(S.I.P.)
Unit II
Permutations & Combinations:
Factorial Notation, Fundamental Theorem,Definition of
Permutations, Simple examples.
Definition of Combinations, Simple examples. Statement of
theorems on Combination. Examples of commercial application of permutations and
combinations.
Linear Programming Problems:
Sketching of graphs of (i) linear equation Ax + By + C =
0 (ii) linear inequalities.
Mathematical Formulation of Linear Programming Problems upto
3 variables. Solution of Linear Programming Problems using graphical method up to 2 variables.
STATISTICS: (36 marks)
Unit III
Measures of Central Tendency:
Arithmetic mean, Weighted mean, Median, Mode, Quartiles,
Deciles and Percentiles. Locating median and quartiles through ogives. Histogram to locate mode, combined mean and
weighted mean.
Measures of Dispersion:
Range, Quartile deviation, Mean deviation from mean,
Standard deviation and their coefficients. Combined standard deviation.
Unit IV
Elementary Probability Theory:
Concept of random experiment/trial and possible outcomes;
Sample Space and Discrete Sample Space; Events their types, Algebra of Events,
Mutually Exclusive and Exhaustive Events, Complimentary events.
Classical definition of Probability, Addition theorem (without
proof), conditional probability.
Independence of Events: P(A∩B) = P(A) P(B) Simple examples.
Random
Variable: Probability distribution of a discrete random variable; Expectation
and Variance; Simple examples on probability distributions.
Unit V
Decision Theory: Decision making situation, Decision
maker, Courses of Action, States of Nature, Pay-off and Pay-off matrix;
Decision making under uncertainty, Maximin, Maximax, Minimax regret and Laplace
criteria; simple examples to find optimum decision. Formulation of Payoff
Matrix.
Decision making under Risk, Expected Monetory Value(EMV);
Decision tree; simple Examples based on EMV, Expected Opportunity Loss(EOL),
simple Examples based on EOL.
Semester II
Course: UBCOMFSII.6
Mathematical and Statistical
Techniques-II
MATHEMATICS : (24 marks)
Unit I
Functions, Derivatives and Their Applications
Concept of real functions: constant function, linear
function, xn , ex,
ax, log x.
Demand, Supply, Total Revenue, Average Revenue, Total cost,
Average cost and Profit function. Equilibrium Point, Break-even point.
Derivative as rate measure.
Derivatives of
functions: Constant function, xn , ex, ax,
log x.
Rules of derivatives: Scalar multiplication, sum,
difference, product, quotient (Statements only), simple problems.
Second Order derivatives
Applications: Derivative as rate of change , Marginal Cost,
Marginal Revenue, Elasticity of Demand. Maxima and Minima for functions in
Economics and Commerce.
(Examination Questions on this unit should be application
oriented only.)
Unit II
Interest and Annuity
Simple Interest and Compound Interest ,Interest compounded more
than once a year. Calculations involving upto 4 time periods.
Annuity Immediate and its Present value, Future value. Equated
Monthly Installments (EMI) using reducing balance method & amortization of
loans. Simple problems involving up to 4 time
periods.
STATISTICS: (36 marks)
Unit III
Bivariate Linear Correlation: Scatter Diagram,
Computation of Karl Pearson’s Coefficient of Correlation(Case of Bivariate
Frequency Table to be excluded), Computation of Spearman’s Rank Correlation
Coefficient (case of repeated ranks upto 2 repetitions only)
Bivariate Linear Regression: Finding Regression lines
by method of least squares. Properties of Regression Coefficients- i) r = √byxbxy ii)
(x̅ , y̅ ) is the point
of intersection of two regression lines.
Unit IV
Time series: Concepts and components of a time
series. Estimation of Trend using Moving Average Method and Least Squares
Method(only Linear Trend)
Estimation of Seasonal Component using Simple Arithmetic
Mean (For Trend free data only)
Concept of Forecasting using Least Squares Method.
Index Numbers: Concept and uses. Simple and Composite
Index Nos. (unweighted, weighted), Laspeyre’s Price Index No, Paasche’s Price
Index No, Fisher’s Price Index No., Cost of living Index No., Real Income,
Simple Examples.
Concept of Wholesale Price Index No. (Examples on missing
values should not be done)
Unit V
Probability
Distributions:
Discrete Probability
Distribution: Binomial ,Poisson (Properties and applications only, no
derivations are expected)
Continuous Probability distribution: Normal Distribution.
(Properties and applications only, no derivations are expected)
Tutorial:
Two tutorials to be conducted on each unit i.e. 10 tutorials per term. At the end of each
term one Tutorial assignment of 10 marks should be given.
Examination:
Internal Assessment 40% (40 marks)
(i)
Two periodical class tests -
20 marks
(ii)
One Tutorial Assignment -
10 marks
(iii)
Active participation in class instructional deliveries
- 05 marks
(iv)
Overall conduct as a responsible student,
mannerism etc. 05 marks.
Semester End Examination 60% (60
marks)
At the end of each semester, there will be a Semester End Examination of 60 marks , 2 hours duration
and question paper pattern as shown below.
Question Paper Pattern:(
Course: UBCOMFSI.6 and Course: UBCOMFSII.6)
1)In Section I (based on Mathematics), Two questions
carrying 12 marks each. First question should be on Unit I and Second question
should be from Unit II.
In each question there should be three sub-questions
carrying 6 marks each . Students should be asked to answer any 2 sub questions
from each question.
2) In Section II
(based on Statistics), Three
questions carrying 12 marks each. First question should be on Unit III , Second
question should be from Unit IV and third question should be from Unit V.
In each question there should be three sub-questions
carrying 6 marks each . Students should be asked to answer any 2 sub questions
from each question.
Reference Books:
1) Mathematics
for Economics and Finance Methods and Modelling by Martin Anthony and Norman
Biggs,
Cambridge University Press, Cambridge
low-priced edition, 2000, Chapters 1, 2, 4, 6 to 9 & 10.
2) Applied
Calculus By Stephen Waner and Steven Constenoble, Brooks/Cole Thomson Learning, second
edition, Chapter 1 to 5.
3) Business
Mathematics By D. C. Sancheti and V. K. Kapoor, Sultan Chand & Sons, 2006,
Chapter 1, 5, 7, 9 &10.
4) Mathematics
for Business Economics
By J. D. Gupta, P. K. Gupta and Man
Mohan, Tata Mc-Graw Hill Publishing Co. Ltd., 1987, Chapters 9 to 11 & 16.
5) Quantitative
Methods-Part-I By S. Saha and S.
Mukerji, New Central Book Agency, 1996, Chapters 7 & 12.
6) Mathematical
Basis of Life Insurance By S.P. Dixit, C.S. Modi and R.V. Joshi,
Insurance Institute of India,
Chapters 2: units 2.6, 2.9, 2.20 & 2.21.
7) Securities
Laws & Regulation of Financial Market
Intermediate Course Paper 8,
Institute of Company Secretaries of India, Chapter 11.
8) Investments
By J.C. Francis & R.W. Taylor,
Schaum’s Outlines, Tata Mc-Graw Hill Edition 2000, Chapters 2,4 & section
25.1.
9) Indian
Mutual Funds Handbook
By Sundar Shankaran, Vision Books,
2006, Sections 1.7,1.8.1, 6.5 & Annexures
1.1to 1.3.
10) STATISTICS
by Schaum Series.
11) Operations
Research by Gupta and Kapoor
12) Operations
Research by Schaum Series
