INDEX 
Subject 
Semester 
Paper Code 
Unit 
Topic 
Format 
Name 
Contact Details 
Date 
Link 
MSCMATH149 P 
Mathematics 
M.Sc SEM –I 
CC1 
Unit 1 
Binary Composition or Binary Relation 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: abhik51@gmail.com 
13.02.2021 

MSCMATH148 P 
Mathematics 
M.Sc SEM –III 
Fluid Dynamics XII (MAT CC12) 
Unit 1 
Convergence of sequence of real functions 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:9430974625 sksuman1575@gmail.com 
06.02.2021 

MSCMATH147 P 
Mathematics 
M.Sc SEM –III 
CC10 
Unit 1 
Infinite Continued fraction 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: abhik51@gmail.com 
06.02.2021 

MSCMATH146 P 
Mathematics 
M.Sc SEM – III 
CC11 
Unit 1 
Problem in Banach space 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: abhaykr378@gmail.com 
30.01.2021 

MSCMATH145 P 
Mathematics 
M.Sc. SemIII, 
CC11 
Unit 1 
Problem in Hilbert space 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:9430974625 abhaykr378@gmail.com 
23.01.2021 

MSCMATH144 P 
Mathematics 
M.Sc. SemIII, 
Fluid Dynamics XII (MAT CC12) 
 
Problems of EOQ with price breaks 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:9430974625 sksuman1575@gmail.com 
23.01.2021 

MSCMATH143 P 
Mathematics 
M.Sc. SemIII, 
CC11 
Unit 1 
Linear Operator Theorem 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: abhik51@gmail.com 
23.01.2021 

MSCMATH142 P 
Mathematics 
M.Sc. SemIII, 
Fluid Dynamics XII (MAT CC12) 
 
Routh’s process for the ignoration of coordinates 
PDF 
Binod Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:9304524851 binodkumararyan@gmail.com 
23.01.2021 

MSCMATH141 P 
Mathematics 
M.Sc. SemIII, Fluid Dynamics XII (MAT CC12) 
Fluid Dynamics XII (MAT CC12) 
 
Problem of EOQ with Finite Replenishment (Production) 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:9430974625 sksuman1575@gmail.com 
16.01.2021 

MSCMATH140 P 
Mathematics 
M.Sc. SemIII, 
Fluid Dynamics XII (MAT CC12) 
 
Concept of Hamiltonian 
PDF 
Binod Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:9304524851 binodkumararyan@gmail.com 
16.01.2021 

MSCMATH139 P 
Mathematics 
M.Sc SEM – III 
CC11 
Unit 1 
Theorem on Hilbert space 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: Email:abhaykr378@gmail.com 
16.01.2021 

MSCMATH138 P 
Mathematics 
M.Sc SEM – III 
CC11 
Unit 1 
Closed graph Theorem 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: Email:abhik51@gmail.com 
16.01.2021 

MSCMATH137 P 
Mathematics 
M.Sc. SemIII, 
Fluid Dynamics XII (MAT CC12) 
 
Multibody dynamics 
PDF 
Binod Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:9304524851 Email:binodkumararyan@gmail.com 
16.01.2021 

MSCMATH136 
Mathematics 
M.Sc Mathematics SEMESTER – III CC11 
CC11 
Unit 1 
Theorem based on Quotient spaces 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: Email:abhik51@gmail.com 
16.01.2021 

MSCMATH135 P 
Mathematics 
M.Sc SEM – III 
CC11 
Unit 1 
Problem on Operator 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: Email: abhaykr378@gmail.com 
16.01.2021 

MSCMATH134 P 
Mathematics 
M.Sc SEM – III 
CC11 
Unit 1 
Systems of inventory control 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: Email: abhaykr378@gmail.com 
28.12.2020 

MSCMATH133 P 
Mathematics 
M.Sc SEM – III 
CC11 
Unit 1 
Reflexive Hilbert space 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: Email: abhaykr378@gmail.com 
28.12.2020 

MSCMATH132 P 
Mathematics 
M.Sc SEM – III 
CC11 
Unit 1 
Problem on projection2 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: Email: abhaykr378@gmail.com 
28.12.2020 

MSCMATH131 P 
Mathematics 
M.Sc SEM – III 
CC11 
Unit 1 
Problem on projection 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: Email: abhaykr378@gmail.com 
28.12.2020 

MSCMATH130 P 
Mathematics 
M.Sc SEM – III 
CC13 
Unit 1 
Spherical indicatrices 
PDF 
Dr. Lok Nath Rai 
Department of Mathematics, Patna University, Patna Mob:9006632911 Email: loknathrai7@gmail.com 
28.12.2020 

MSCMATH129 P 
Mathematics 
M.Sc. SemIII 
 
 
Inventory problems with uncertain demand 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:9304524851 Email: binodkumararyan@gmail.com 
28.12.2020 

MSCMATH128 P 
Mathematics 
M.Sc. SemIII, Fluid Dynamics XII (MAT CC12) 
Fluid Dynamics XII (MAT CC12) 
 
Vortex Motion(Rectilinear Vortices) 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:9304524851 Email: binodkumararyan@gmail.com 
19.12.2020 

MSCMATH127 P 
Mathematics 
M.Sc. SemIII 
 
 
Inventory control continued 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:9430974625 Email: sksuman1575@gmail.com 
12.12.2020 

MSCMATH126 P 
Mathematics 
M.Sc. SemIII 
 
 
Evolute and its curvature and torsion expressions 
PDF 
Dr. Lok Nath Rai 
Department of Mathematics, Patna University, Patna Mob:9006632911 Email: loknathrai7@gmail.com 
12.12.2020 

MSCMATH125 P 
Mathematics 
M.Sc. SemIII 
 
 
Theorem based on Hilbert space is isometric and isomorphic to the complex space 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: Email: abhik51@gmail.com 
12.12.2020 

MSCMATH124 P 
Mathematics 
M.Sc. SemIII 
 
 
General Solution of Laplace equation in spherical coordinate 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9430974625 Email: sksuman1575@gmail.com 
12.12.2020 

MSCMATH123 P 
Mathematics 
M.Sc. SemIII, 
Fluid Dynamics XII (MAT CC12) 
 
General Solution of Laplace equation in spherical coordinate 
PDF 
Binod Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9304524851 Email: binodkumararyan@gmail.com 
12.12.2020 

MSCMATH122 P 
Mathematics 
M.Sc SEM– III 
CC11 
Unit 1 
Principle of uniform boundedness or Banach Steinhaus 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: Email: abhik51@gmail.com 
30.11.2020 

MSCMATH121 P 
Mathematics 
M.Sc. SemIII 
Fluid Dynamics XII (MAT CC12) 
 
Motion of a sphere 
PDF 
Binod Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9304524851 Email: binodkumararyan@gmail.com 
30.11.2020 

MSCMATH121 P 
Mathematics 
M.Sc Mathematics SEMESTER – III CC13 Unit 1 
CC13 
Unit 1 
Differential Geometry 
PDF 
Dr. Lok Nath Rai 
Department of Mathematics, Patna University, Patna Mob: 9006632911 Email: loknathrai7@gmail.com 
30.11.2020 

MSCMATH120 P 
Mathematics 
M.Sc Mathematics Semester – III 
 
 
Inventory control 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9430974625 Email: sksuman1575@gmail.com 
30.11.2020 

MSCMATH119 P 
Mathematics 
M.Sc Sem – III 
 
 
Factors affecting inventory control 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9430974625 Email: sksuman1575@gmail.com 
30.11.2020 

MSCMATH118 P 
Mathematics 
M.Sc SEM – III 
CC11 
Unit 1 
Theorem based on Hilbert Space 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: Email: abhik51@gmail.com 
30.11.2020 

MSCMATH117 P 
Mathematics 
M.Sc SEM – III 
CC11 
Unit 5 
Theorem and problem on projection 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: Email: abhaykr378@gmail.com 
28.11.2020 

MSCMATH116 P 
Mathematics 
M.Sc Sem – III 
 
 
GAME THEORYIII 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9430974625 Email: sksuman1575@gmail.com 
12.11.2020 

MSCMATH115 P 
Mathematics 
M.Sc SEM– III 
C11 
Unit 5 
Theorem on projection 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: Email: abhaykr378@gmail.com 
12.11.2020 

MSCMATH114 P 
Mathematics 
M.Sc SEM – III 
CC11 
Unit 5 
Theorem and problems on Normal and Unitary operators 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: Email: abhaykr378@gmail.com 
12.11.2020 

MSCMATH113 P 
Mathematics 
M.Sc Mathematics SEMESTER – III 
CC11 
Unit 1 ww 
Theorem based on Inner Product Space 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: Email: abhik51@gmail.com 
12.11.2020 

MSCMATH112 P 
Mathematics 
M.Sc. SemIII, Fluid Dynamics XII (MAT CC12) 


General concept of motion of Cylinders 
PDF 
Binod Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9304524851 Email: binodkumararyan@gmail.com 
12.11.2020 

MSCMATH111 P 
Mathematics 
M.Sc. SemIII, 
Fluid Dynamics XII (MAT CC12) 
 
Motion of a circular cylinder 
PDF 
Binod Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9304524851 Email: binodkumararyan@gmail.com 
12.11.2020 

MSCMATH110 P 
Mathematics 
M.Sc Seme – III 
 
 
Games Without Saddle Points – Mixed Strategies 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9430974625 Email: sksuman1575@gmail.com 
10.11.2020 

MSCMATH109 P 
Mathematics 
M.Sc SEM – III 
CC13 
Unit 1 
Betrand Curves and other properties 
PDF 
Dr. Lok Nath Rai 
Department of Mathematics, Patna University, Patna Mob: 9006632911 Email: loknathrai7@gmail.com 
10.11.2020 

MSCMATH108 P 
Mathematics 
M.Sc Mathematics SEMESTER – III 
CC13 
Unit 1 
Define Betrand Curves 
PDF 
Dr. Lok Nath Rai 
Department of Mathematics, Patna University, Patna Mob: 9006632911 Email: loknathrai7@gmail.com 
06.11.2020 

MSCMATH107 P 
Mathematics 
M.Sc Mathematics SEMESTER – III 
CC11 
Unit 1 
Theorem based on absolutely summable series 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhik51@gmail.com 
06.11.2020 

MSCMATH106 P 
Mathematics 
M.Sc. SemIII, 
Fluid Dynamics XII (MAT CC12) 
 
The Theorem of Blasius 
PDF 
Binod Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9304524851 Email: binodkumararyan@gmail.com 
06.11.2020 

MSCMATH105 P 
Mathematics 
M.Sc. SemIII 
Fluid Dynamics XII (MAT C12C) 
 
Simply the circle theorem 
PDF 
Binod Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9304524851 Email: binodkumararyan@gmail.com 
31.10.2020 

MSCMATH104 P 
Mathematics 
M.Sc SEM – III 
CC11 
Unit 1 
Theorem based on Projection on Banach spaces 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: Email: abhik51@gmail.com 
31.10.2020 

MSCMATH103
P 
Mathematics 
M.Sc SEM – III 
CC11 
Unit 1 
Projection on Banach spaces 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: Email: abhik51@gmail.com 
31.10.2020 

MSCMATH102 P 
Mathematics 
M.Sc SEM – III 
CC11 
Unit 1 
Cylindrical helix 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: Email: abhik51@gmail.com 
31.10.2020 

MSCMATH101 P 
Mathematics 
M.Sc Mathematics SEM– III 
CC11 
Unit 5 
Normal and Unitary Operators 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: Email: abhaykr378@gmail.com 
31.10.2020 

MSCMATH100 P 
Mathematics 
M.Sc Mathematics SEMESTER – III 
CC11 
Unit 5 
Normal operators 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: Email: abhaykr378@gmail.com 
31.10.2020 

MSCMATH099 P 
Mathematics 
M.Sc. SemIII, 
Fluid Dynamics XII (MAT CC12) 
 
Complex Potential for Irrotational Motion in Twodimensions 
PDF 
Binod Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9304524851 Email: binodkumararyan@gmail.com 
31.10.2020 

MSCMATH098 P 
Mathematics 
M.Sc Sem– III 
 
 
Game theory 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9430974625 Email: sksuman1575@gmail.com 
28.10.2020 

MSCMATH097 P 
Mathematics 
M.Sc SEM – III 
CC11 
Unit 4 
Positive Operators 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhaykr378@gmail.com 
22.10.2020 

MSCMATH096 P 
Mathematics 
M.Sc SEM – III 
CC13 
Unit 1 
Serret Frenet formula 
PDF 
Dr. Lok Nath Rai 
Department of Mathematics, Patna University, Patna Mob: 9006632911 Email: loknathrai7@gmail.com 
22.10.2020 

MSCMATH095
P 
Mathematics 
M.Sc SEM – III 
CC11 
Unit 1 
Theorem based on finitedimensional 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhik51@gmail.com 
22.10.2020 

MSCMATH094 P 
Mathematics 
M.Sc SEM – III 
CC11 
Unit 4 
Theorems on operator and self adjoint operators. 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhaykr378@gmail.com 
22.10.2020 

MSCMATH093 P 
Mathematics 
M.Sc Sem – III, 
 
 
Nonlinear programming problems 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9430974625 Email: sksuman1575@gmail.com 
22.10.2020 

MSCMATH092 P 
Mathematics 
M.Sc SEM – III 
CC11 
Unit 4 
Theorems on self –adjoint operators 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhaykr378@gmail.com 
22.10.2020 

MSCMATH091 P 
Mathematics 
M.Sc SEM – III 
CC11 
Unit 1 
Example of Conjugate Space 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhik51@gmail.com 
16.10.2020 

MSCMATH090 P 
Mathematics 
M.Sc. SemIII, 
Fluid DynamicIs XI (MAT CC12) 
 
Motion in TwoDimensions Source and Sink 
PDF 
Binod Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9304524851 Email: binodkumararyan@gmail.com 
16.10.2020 

MSCMATH089 P 
Mathematics 
M.Sc. SemIII, 
Fluid Dynamics XII (MAT CC12) 
 
Bernoulli’s equation and its application 
PDF 
Binod Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9304524851 Email: binodkumararyan@gmail.com 
16.10.2020 

MSCMATH088 P 
Mathematics 
M.Sc Mathematics Semester – III, 
 
 
Wolfe’s Modified Simplex Method 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9430974625 Email: sksuman1575@gmail.com 
16.10.2020 

MSCMATH087 P 
Mathematics 
M.Sc SEM – III 
CC11 
Unit 4 
Problems on Adjoint Operator 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhaykr378@gmail.com 
16.10.2020 

MSCMATH086
P 
Mathematics 
M.Sc Mathematics SEMESTER – III 
CC11 
Unit 1 
Dual Space or (conjugate space) 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhik51@gmail.com 
16.10.2020 

MSCMATH085 P 
Mathematics 
M.Sc Mathematics SEMESTER – III 
CC11 
Unit 4 
The Adjoint Operator 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhaykr378@gmail.com 
16.10.2020 

MSCMATH084 P 
Mathematics 
M.Sc SEM – III 
CC11 
Unit 4 
A characterization theorem for complete orthonormal sets 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhaykr378@gmail.com 
10.10.2020 

MSCMATH083 P 
Mathematics 
Sem – III, 
 
 
KarushKuhnTucker (KKT) Conditions 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9430974625 Email: sksuman1575@gmail.com 
10.10.2020 

MSCMATH083 P 
Mathematics 
SEMESTER – III 
CC11 
Unit 4 
FrechetRiesz representation theorem 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhaykr378@gmail.com 
07.10.2020 

MSCMATH082 P 
Mathematics 
SEMESTER – III 
CC13 
Unit 1 
Differential Geometry 
PDF 
Dr. Lok Nath Rai 
Department of Mathematics, Patna University, Patna Mob: 9006632911 Email: loknathrai7@gmail.com 
30.09.2020 

MSCMATH081 P 
Mathematics 
SEMESTER – III 
CC11 
Unit 4 
Bessel′s Inequality 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhaykr378@gmail.com 
30.09.2020 

MSCMATH080 P 
Mathematics 
M.Sc. SemIII 
Fluid Dynamics XII (MAT CC12 
 
Euler’s equation of motion 
PDF 
Binod Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9304524851 Email: binodkumararyan@gmail.com 
30.09.2020 

MSCMATH079 P 
Mathematics 
M.Sc. SemIII, 
Fluid Dynamics XII (MAT CC12) 
 
Rotational and irrotional fluid flow 
PDF 
Binod Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9304524851 Email: binodkumararyan@gmail.com 
30.09.2020 

MSCMATH078 P 
Mathematics 
M.Sc. SemIII, ) 
Fluid Dynamics XII (MAT CC12) 
 
Lamb’s hydrodynamical equation 
PDF 
Binod Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9304524851 Email: binodkumararyan@gmail.com 
30.09.2020 

MSCMATH077 P 
Mathematics 
M.Sc. SemIII, 
Fluid Dynamics XII (MAT CC12) 
 
Equation of motion under impulsive forces 
PDF 
Binod Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9304524851 Email: binodkumararyan@gmail.com 
30.09.2020 

MSCMATH076 P 
Mathematics 
M.Sc. SemIII, 
Fluid Dynamics XII (MAT CC12) 
 
The energy equation and example 
PDF 
Binod Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9304524851 Email: binodkumararyan@gmail.com 
30.09.2020 

MSCMATH075 P 
Mathematics 
Semester – III, 
 
 
Interior Point Algorithms 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9430974625 Email: sksuman1575@gmail.com 
25.09.2020 

MSCMATH074 P 
Mathematics 
Sem – III, 
 
 
Simplex method for goal programming problem 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9430974625 Email: sksuman1575@gmail.com 
25.09.2020 

MSCMATH073 P 
Mathematics 
SEM– III 
CC11 
Unit 1 
Theorem based on linear transformation 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhik51@gmail.com 
25.09.2020 

MSCMATH072 P 
Mathematics 
SEM– III 
CC11 
Unit 4 
Projection theorem in a Hilbert space 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhaykr378@gmail.com 
24.09.2020 

MSCMATH071 P 
Mathematics 
SEM – III 
CC11 
Unit 1 
Equivalent Norms 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhik51@gmail.com 
24.09.2020 

MSCMATH070 P 
Mathematics 
SEM – III 
CC13 
Unit 1 
Equation of motion for a simple pendulum 
PDF 
Dr. Lok Nath Rai 
Department of Mathematics, Patna University, Patna Mob: 9006632911 Email: loknathrai7@gmail.com 
24.09.2020 

MSCMATH069 P 
Mathematics 
SEMESTER – III, 
CC11(functional analysis) 
Unit4 
Theorem on the Hilbert Space 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhaykr378@gmail.com 
15.09.2020 

MSCMATH068 P68 
Mathematics 
Semester – III, 
 
 
Integer programming problem 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9430974625 Email: sksuman1575@gmail.com 
15.09.2020 

MSCMATH067 P 
Mathematics 
SEMESTER – III, 
CC11, 
Unit4 
Theorem on Hilbert space 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhaykr378@gmail.com 
15.09.2020 

MSCMATH066 P 
Mathematics 
SEM – III, 
CC11, 
Unit4 
Convex set in a linear space 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhaykr378@gmail.com 
15.09.2020 

MSCMATH065 P 
Mathematics 
SEM – III 
CC11 
Unit1 
Functional AnalysisL7 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhik51@gmail.com 
15.09.2020 

MSCMATH064 P 
Mathematics 
SEMESTER – III 
 
 
Integer Programming Problem 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9430974625 Email: sksuman1575@gmail.com 
08.09.2020 

MSCMATH063 P 
Mathematics 
SEMESTER – III 
CC13 
Unit 1 
Obtain Lagrange’s differential equation for holonomic dynamical system 
PDF 
Dr. Lok Nath Rai 
Department of Mathematics, Patna University, Patna Mob: 9006632911 Email: loknathrai7@gmail.com 
08.09.2020 

MSCMATH062 P 
Mathematics 
SEMESTER – III 
CC11 
Unit4 
Construct an example of a normed linear space which is not a Banach space 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhik51@gmail.com 
08.09.2020 

MSCMATH061 P 
Mathematics 
SEMESTER – III 
CC11, 
Unit4 
Theorem and problem based on the Hilbert space 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhaykr378@gmail.com 
04.09.2020 

MSCMATH060 P 
Mathematics 
SEMESTER – III 
CC11, 
Unit4 
Theorems based on the Hilbert Spaces 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhaykr378@gmail.com 
27.08.2020 

MSCMATH059 P 
Mathematics 
– III 
CC11 
Unit4 
Problems based on inner product space 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhik51@gmail.com 
27.08.2020 

MSCMATH058 P 
Mathematics 
SEM– III 
CC11 
Unit 1 
Banach space 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhik51@gmail.com 
22.08.2020 

MSCMATH057 P 
Mathematics 
SEMESTER – III 
CC11 
Unit 1 
Functional Analysisis cauchy sequence,Continuous function and Theorem 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhik51@gmail.com 
22.08.2020 

MSCMATH056 P 
Mathematics 
SEM– III 
CC13 
Unit 1 
Generalised Coordinates 
PDF 
Dr. Lok Nath Rai 
Department of Mathematics, Patna University, Patna Mob:  9006632911 Email: loknathrai7@gmail.com 
22.08.2020 

MSCMATH055 P 
Mathematics 
SemIII, 
Paper: Fluid Dynamics XII (MAT CC12) 
 
Parametric Linear Programming 
PDF 
Binod Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  9304524851 Email: binodkumararyan@gmail.com 
22.08.2020 

MSCMATH054 P 
Mathematics 
SEM – III 
 
 
Parametric Linear Programming 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  9430974625 Email: sksuman1575@gmail.com 
22.08.2020 

MSCMATH053 P 
Mathematics 
SEM – III) 
CC11, 
Unit4 
Theorem based on inner product spaces and Hilbert spaces 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhaykr378@gmail.com 
22.08.2020 

MSCMATH052 P 
Mathematics 
SemIII, 
Fluid Dynamics XII (MAT CC12) 
 
Equation of continuity by Lagrangian Approach 
PDF 
Binod Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9304524851 Email: binodkumararyan@gmail.com 
22.08.2020 

MSCMATH051 P 
Mathematics 
SEMESTER – III 
 
 
Dual Problem 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9430974625 Email: sksuman1575@gmail.com 
22.08.2020 

MSCMATH050 P 
Mathematics 
SEM – III 
CC13 
Unit 1 
Rigid Dynamics 
PDF 
Dr. Lok Nath Rai 
Department of Mathematics, Patna University, Patna Mob: 9006632911 Email: loknathrai7@gmail.com 
22.08.2020 

MSCMATH049 P 
Mathematics 
SEMESTER – III 
CC11 
Unit 1 
Functional Analysis 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhaykr378@gmail.com 
22.08.2020 

MSCMATH048 P 
Mathematics 
SEMESTER – III, ) 
CC11, 
Unit4 
Inner Product Spaces 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhaykr378@gmail.com 
19.08.2020 

MSCMATH047 P 
Mathematics 
SEMESTER – II 
CC11 
Unit 1 
Linear Space (Vector Space) 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhaykr378@gmail.com 
14.08.2020 

MSCMATH046 P46 
Mathematics 
M.Sc. SemIII, 
Fluid Dynamics XII (MAT CC12) 
 
Equation of continuity in Coordinate system 
PDF 
Binod Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9304524851 Email: binodkumararyan@gmail.com 
13.08.2020 

MSCMATH045 P 
Mathematics 
M.Sc. SemIII, 
Fluid Dynamics XII (MAT CC12) 
 
Material derivatives and Euler equation of continuity 
PDF 
Binod Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9304524851 Email: binodkumararyan@gmail.com 
13.08.2020 

MSCMATH044 P 
Mathematics 
M.Sc. SemIII, 
Fluid Dynamics XII (MAT CC12) 
 
Lagrangian and Eulerian flow 
PDF 
Binod Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9304524851 Email: binodkumararyan@gmail.com 
13.08.2020 

MSCMATH043 P 
Mathematics 
SemIII 
 
 
LPP (Simplex Method)3 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9430974625 Email: sksuman1575@gmail.com 
13.08.2020 

MSCMATH082 P42 
Mathematics 
SemIII 
 
 
LPP (Simplex Method)2 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9430974625 Email: sksuman1575@gmail.com 
07.08.2020 

41 
Mathematics 
SEMESTER – II 
CC11 
Unit 1 
Functional Analysis 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhaykr378@gmail.com 
07.08.2020 

MSCMATH040 P 
Mathematics 
SEM – II,( 
CC – 09 
Topology 
The Tietze Extension Theorem 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhaykr378@gmail.com 
07.08.2020 

39 
Mathematics 
M.Sc. SemIII 
 
 
LPP (Simplex Method) 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9430974625 Email: sksuman1575@gmail.com 
30.07.2020 

38 
Mathematics 
Sem 2 
CC 11, 
Unit 1 
Linear Space 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhaykr378@gmail.com 
30.07.2020 

37 
Mathematics 
Semester: II,) 
Paper VII (MAT CC07 
 
Fredhlom integral equation 
PDF 
Binod Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9304524851 Email: binodkumararyan@gmail.com 
30.07.2020 

MSCMATH030 P 
Mathematics 
Semester: II, 
Paper VII (MAT CC07) 
 
Resolvent Kernal 
PDF 
Binod Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9304524851 Email: binodkumararyan@gmail.com 
30.07.2020 

MSCMATH035 P 
Mathematics 
M.Sc. SemIII 
 
 
General Linear Programming Problem 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9430974625 Email: sksuman1575@gmail.com 
24.07.2020 

MSCMATH034 P 
Mathematics 
M.Sc. SemII 
 
 
Complex Integration 
PDF 
Dr. Lok Nath Rai 
Department of Mathematics, Patna University, Patna Mob: 9006632911 Email: loknathrai7@gmail.com 
17.07.2020 

MSCMATH033 P 
Mathematics 
M.Sc. Mathematics Semester: IV, 
Paper (MAT EC02)) 
 
Galois finite field concept 
PDF 
Binod Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9304524851 Email: binodkumararyan@gmail.com 
17.07.2020 

MSCMATH032 P 
Mathematics 
M.Sc. Mathematics Semester: II, 
Paper VII (MAT CC07) 
 
Differential Inequality 
PDF 
Binod Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9304524851 Email: binodkumararyan@gmail.com 
17.07.2020 

MSCMATH032 P 
Mathematics 
Mathematics Semester: II,) 
PaperVII (MAT CC07 
 
Osgood and Nagumo Theorem 
PDF 
Binod Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9304524851 Email: binodkumararyan@gmail.com 
17.07.2020 

MSCMATH030 P 
Mathematics 
M.Sc. SemIV 
 
 
Galois Theory 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9430974625 Email: sksuman1575@gmail.com 
17.07.2020 

MSCMATH029 P 
Mathematics 
M.Sc. SemII 
 
 
Cantor theory and outer measure 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9430974625 Email: sksuman1575@gmail.com 
17.07.2020 

MSCMATH028 P 
Mathematics 
M.Sc Semester4 
Elective Paper –Mathematical Method 
 
Partial differential equation 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhaykr378@gmail.com 
17.07.2020 

MSCMATH027 P 
Mathematics 
M.Sc Sem 2 
CC 10, 
Unit 4 
Number Theory2nd Part 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhaykr378@gmail.com 
17.07.2020 

MSCMATH026 P 
Mathematics 
M.Sc Sem 2 , 
CC 10 
Unit 4 
Number Theory1st Part 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhaykr378@gmail.com 
17.07.2020 

MSCMATH025 P 
Mathematics 
M.Sc Sem 2 
CC 10, 
Unit 4 
Infinite Continued Fractions 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhaykr378@gmail.com 
28.05.2020 

MSCMATH024 P 
Mathematics 
M.Sc. SemII 
 
 
Extension Of Measure 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9430974625 Email: sksuman1575@gmail.com 
28.05.2020 

MSCMATH023 
Mathematics 
M.Sc. SemII 
 
 
Uniqueness Of The Extension 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9430974625 Email: sksuman1575@gmail.com 
28.05.2020 

MSCMATH022 p 
Mathematics 
SemII 
 
 
Contour Integration Continued 
PDF 
Dr. Lok Nath Rai 
Department of Mathematics, Patna University, Patna Mob: 9006632911 Email: loknathrai7@gmail.com 
28.05.2020 

MSCMATH021 P 
Mathematics 
M.Sc SEM 2 Unit 4 
CC 10 
Unit 4 
Continued Fraction 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhaykr378@gmail.com 
22.05.2020 

MSCMATH020 P 
Mathematics 
M.Sc Mathematics SEMESTER – II, 
CC – 09(Topology) 
 
Urysohn's lemma 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhaykr378@gmail.com 
22.05.2020 

MSCMATH018 P 
Mathematics 
M.Sc. SemII 
 
 
Countour Integration 
PDF 
Dr. Lok Nath Rai 
Department of Mathematics, Patna University, Patna Mob: 9006632911 Email: loknathrai7@gmail.com 
15.05.2020 

MSCMATH019 P 
Mathematics 
M.Sc SEM 2 
CC 10 
Unit 4 
Farey Series 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: Email: loknathrai7@gmail.com 
15.05.2020 

MSCMATH017 
Mathematics 
M.Sc. Mathematics Semester: II, 
Paper VII (MAT CC07) 
 
Differential and integral Equation 
PDF 
Binod Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9304524851 Email: binodkumararyan@gmail.com 
15.05.2020 

MSCMATH016 P 
Mathematics 
M.Sc SemIV 
 
 
Interior Dirichlet Problem For A Circle 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9430974625 Email: sksuman1575@gmail.com 
15.05.2020 

MSCMATH015 P 
Mathematics 
M.Sc Mathematics SemIV 
 
 
General Nature Of Boundary Value Problems 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9430974625 Email: sksuman1575@gmail.com 
15.05.2020 

MSCMATH014 P 
Mathematics 
M.Sc SEM 2 
CC 10, 
Unit 2 
Hurwitz Theorem 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: loknathrai7@gmail.com 
09052020 

MSCMATH013 P 
Mathematics 
M.Sc SEM 2 
CC 10 
Unit 4 
Hurwitz Theorem 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: loknathrai7@gmail.com 
09052020 

MSCMATH012 P 
Mathematics 
M.Sc SemIV 
 
 
Bessel's Equation 
PDF 
Dr Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhaykr378@gmail.com 
26042020 

MSCMATH011 P 
Mathematics 
M.S c Mathematics –SEM 2 CC 10 
CC 10 
 
Number Theory 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: loknathrai7@gmail.com 
26042020 

MSCMATH010 P 
Mathematics 
M.S c Mathematics SemIV 
 
 
Weierstrass Approximation Theorem 
PDF 
Abhay Kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: abhaykr378@gmail.com 
26042020 

MSCMATH009 P 
Mathematics 
M.S c Mathematics SemIV 
 
 
Partial Differential Equation 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9430974625 Email: sksuman1575@gmail.com 
26042020 

MSCMATH008 P 
Mathematics 
M.Sc SemIV 
 
 
The Four Derivates 
PDF 
Shailednra Pandit (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9430974625 Email: sksuman1575@gmail.com 
26042020 

MSCMATH007 P 
Mathematics 
M.S c Mathematics 
 
 
singularity(cavity) 
PDF 
Binod kumar (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob:  Email: binodkumararyan@gmail.com 
26042020 

MSCMATH006 P 
Mathematics 
M.Sc SEM 2 
CC 10 
 
Mobius Function 
PDF 
Dr Abhik Singh (Guest faculty) 
Department of Mathematics, Patna University, Patna Mob: 9006632911 Email: loknathrai7@gmail.com 
16042020 

MSCMATH005 P 
Mathematics 
M.Sc. Sem 4 
EC07 
 
Mathematical Methods 
PDF 
Dr. Lok Nath Rai 
Department of Mathematics, Patna University, Patna
Mob: 9006632911
Email: loknathrai7@gmail.com 
15042020 

MSCMATH004 P 
Mathematics 
M.Sc SEM 2 
MEASURE THEORY 
 
L^{P }Spaces 
PDF 
Shailednra Pandit (Guest Faculty) 
Department of Mathematics, Patna University, Patna
Mob: 9430974625
Email: sksuman1575@gmail.com 
13042020 

MSCMATH003 P 
Mathematics 
M.Sc SEM 2 
MEASURE THEORY 
 
Absolutely Continuous functions 
PDF 
Shailednra Pandit Guest Faculty 
Department of Mathematics, Patna University, Patna
Mob: 9430974625
Email: sksuman1575@gmail.com 
13042020 

MSCMATH002 P 
Mathematics 
M.Sc SEM 2 
MEASURE THEORY 
 
Integration of nonnegative functions 
PDF 
Shailednra Pandit (Guest Faculty) 
Department of Mathematics, Patna University, Patna
Mob: 9430974625
Email: sksuman1575@gmail.com 
13042020 

MSCMATH001 P 
Mathematics 
M.S c Mathematics –SEM 2 
 
CC 10 
Number Theory 
PDF 
Dr Abhik Singh (Guest Faculty) 
Department of Mathematics, Patna University, Patna
Email: loknathrai7@gmail.com 
13042020 
