Bsc Maths Part III Syllabus
Bsc Maths Part III Syllabus 2022
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BSc Maths part III consists of three papers in which paper I includes book Real Analysis And Theory of Convergence. Paper II includes Higher Complex . And Paper III includes Linear Programming problems and Optimisation Techniques.
Here I will provide you all the important topics and exam pattern of Bsc maths part III.
Here I will provide you all the important topics and exam pattern of Bsc maths part III.
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Exam pattern
M.D.S. University, AJMER
B.Sc. Part III Examination
Duration: 3Hrs.
Max.Marks: 75
Note 1. Common paper will be set for both the faculties of Social sciences and
Science. However the marks obtained by candidates in the faculty of
Social sciences will be converted according to the ratio of the maximum
marks of the paper in two faculties.
Note 2. The paper is divided into three independent units. The question paper
is divided into 'Three parts Part-A, Part-B and Part-C.
Part A- (15 Marks) is compulsory and contains 10 questions (50 words) at
least 3 questions from each unit, each question is of 1.5 marks.
Part B- (15 Marks) is compulsory and contains 5 questions (100 words) at
least one question from each unit, each question is of 3 marks.
Part C- (45 Marks) contains 6 questions two from each unit. The candidate
is required to attempt 3 questions one from each Unit. Each question
is of 15 marks (400 words).
B.Sc. Part III Examination
Duration: 3Hrs.
Max.Marks: 75
Note 1. Common paper will be set for both the faculties of Social sciences and
Science. However the marks obtained by candidates in the faculty of
Social sciences will be converted according to the ratio of the maximum
marks of the paper in two faculties.
Note 2. The paper is divided into three independent units. The question paper
is divided into 'Three parts Part-A, Part-B and Part-C.
Part A- (15 Marks) is compulsory and contains 10 questions (50 words) at
least 3 questions from each unit, each question is of 1.5 marks.
Part B- (15 Marks) is compulsory and contains 5 questions (100 words) at
least one question from each unit, each question is of 3 marks.
Part C- (45 Marks) contains 6 questions two from each unit. The candidate
is required to attempt 3 questions one from each Unit. Each question
is of 15 marks (400 words).
๐๐๐๐๐
Paper I Syllabus and Important Topics
Book 1 (Real Analysis)
UNIT-I
Real number system as a complete ordered field:
The point set theory, open and closed sets,limit point of a set,
neighborhoods, Bolzano-Weierstrass theorem, Heine-Borel theorem,
compactness, connectedness, cantor's ternary set,
E- delta definition of the limit of a function, basic properties of limits, continuous functions and classification of discontinuities,
sequential continuity, properties of continuous functions defined on closed intervals, limit and continuity' of functions of TWO variables.
UNIT II
Differentiability, properties of different
theorems and their geometrical interpretation, Darboux intermediate theorem for derivatives, Taylor's theorem for functions of TWO variables.
CONTENTS
UNIT-I
Real number system as a complete ordered field:
The point set theory, open and closed sets,limit point of a set,
neighborhoods, Bolzano-Weierstrass theorem, Heine-Borel theorem,
compactness, connectedness, cantor's ternary set,
E- delta definition of the limit of a function, basic properties of limits, continuous functions and classification of discontinuities,
sequential continuity, properties of continuous functions defined on closed intervals, limit and continuity' of functions of TWO variables.
UNIT II
Differentiability, properties of different
theorems and their geometrical interpretation, Darboux intermediate theorem for derivatives, Taylor's theorem for functions of TWO variables.
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CONTENTS
Chapters
Part I (Real Analysis)
1. Real Number System
2. The Point Set Theory
Part II (Advanced Differential Calculus)
1. Limit
2. Continuity
3. Differentiability
4. Mean Value Theorems
Part-III (Advanced Integral Calculus)
1. Riemann Integral
● Reference
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Book 2 ( Theory of Convergence)
UNIT II
Definition of a sequence, theorems on limits of sequences, bounded and monotonic sequences, Cauchy's convergence criterion.
UNIT III
UNIT III
Infinite series of non-negative terms, its convergence, different tests
of convergence of infinite series i.e. comparison tests, Cauchy's integral tests, Ratio tests, Raabe's, Logarithmic, DeMorgan and Bertrand's tests (without proof), Alternating series test, Leibnitz's theorem, absolute and conditional convergence,
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Fourier series, Fourier expansion of piecewise monotonic functions, Uniform convergence of Series of Functions, Wierstrass M-test, Abel's test and Dirichlet's test.
CONTENTS
Chapters
1. Convergence of Real Sequences
2. Convergence of Infinite Series
3. Uniform Convergence
4. Convergence of Improper Integrals
5. Fourier Series
Paper II Syllabus And Important Topics
of convergence of infinite series i.e. comparison tests, Cauchy's integral tests, Ratio tests, Raabe's, Logarithmic, DeMorgan and Bertrand's tests (without proof), Alternating series test, Leibnitz's theorem, absolute and conditional convergence,
๐๐๐๐
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Fourier series, Fourier expansion of piecewise monotonic functions, Uniform convergence of Series of Functions, Wierstrass M-test, Abel's test and Dirichlet's test.
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CONTENTS
Chapters
1. Convergence of Real Sequences
2. Convergence of Infinite Series
3. Uniform Convergence
4. Convergence of Improper Integrals
5. Fourier Series
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Paper II Syllabus And Important Topics
(COMPLEX ANALYSIS)
Unit - I
Complex Numbers as ordered pairs, Complex plane, Geometrical
representation of complex numbers, conjugate complex numbers, Connected
and compact sets, Curves and region in the complex plane, Statement of
Jordan curves theorem, Extended complex plane and stereographic projection,
Complex valued functions limits and continuity, Convergence,
Differentiailbility in the extended plane, Analytic functions. Cauchy- Reimann
equations (Cartesian and Polar forms). Complex equation of a Straight line
and circle, Polynomials, multivalued functions, Harmonic functions.
representation of complex numbers, conjugate complex numbers, Connected
and compact sets, Curves and region in the complex plane, Statement of
Jordan curves theorem, Extended complex plane and stereographic projection,
Complex valued functions limits and continuity, Convergence,
Differentiailbility in the extended plane, Analytic functions. Cauchy- Reimann
equations (Cartesian and Polar forms). Complex equation of a Straight line
and circle, Polynomials, multivalued functions, Harmonic functions.
Unit II
mapping, necessary and sufficient condition for w = f(z) to represent
conformal mapping some elementry transformations, Bilinear transformation
and its properties, Fixed points, Cross ratio, Inverse point, Elementary maps:
F (2) = 2²¹; √z, 1 (2+1), sin z, log z
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Unit III
reduction of complex integrals
real integrals, properties of complex
integrals, Cauchy's fundamental theorem, Cauchy's integral formula,
derivative of an analytic function, Morera's theorem. Liouville's theorem,
Poisson's integral formula, expansion of analytic functions as power series,
Taylor's and Laurent's theorems.
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CONTENTS
Chapters
Part I
1. Complex Numbers
2. Sets in Complex Plane
3. Complex Functions, Limit and Continuity
4. Complex Differentiation
5. Conformal Mapping
2. Sets in Complex Plane
3. Complex Functions, Limit and Continuity
4. Complex Differentiation
5. Conformal Mapping
Part II
1. Complex Integration
2. Applications of Cauchy's Integral Theorem
Formation of LPP, graphical solution, convex set and its properties, Feasible solution, Basic solution, Optimal solution, Simplex method, Big M-method, Two phase method.
Degeneracy in simplex method, and its resolution, Revised simplex method, concept of Duality in LPP, Formulation of dual problems, Elementary theorems of Duality.
Introduction of allocation problems, Assignment Problem, Hungarian method, minimum row cover method, unbalanced assignment problems.
Transportation Problem, North-West corner method, lowest cost entry method, Vogel's approximation method, degeneracy and optimal solution of transportation problem.
Game thoery, fundamental principle, saddle point, dominance rule, graphical method for solution of 2 x n and m x 2 games, solution of
a rectangular game by simplex method.
2. Applications of Cauchy's Integral Theorem
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Paper III Syllabus AND Important Topics
(Optimization Techniques)
UNIT I
UNIT II
Degeneracy in simplex method, and its resolution, Revised simplex method, concept of Duality in LPP, Formulation of dual problems, Elementary theorems of Duality.
UNIT III
Introduction of allocation problems, Assignment Problem, Hungarian method, minimum row cover method, unbalanced assignment problems.
Transportation Problem, North-West corner method, lowest cost entry method, Vogel's approximation method, degeneracy and optimal solution of transportation problem.
Game thoery, fundamental principle, saddle point, dominance rule, graphical method for solution of 2 x n and m x 2 games, solution of
a rectangular game by simplex method.
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M.D.S. University, AJMER
CONTENTS
Chapters
1. Linear Programming Problems
2. Basic Concepts
3. Theory of Simplex Method
4. Simplex Algorithm
5. Duality
Part I (LPP)
1. Linear Programming Problems
2. Basic Concepts
3. Theory of Simplex Method
4. Simplex Algorithm
5. Duality
6. Generalised Simplex Method
7. Revised Simplex Method
7. Revised Simplex Method
Part II (OT)
2. Transportation Problems
3. Game Theory
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