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M. S. P. Mandal's Vinayakrao Patil Mahavidyalaya, Vaijapur

College with Potential for Excellence || STRIDE and Paramarsh Schemes by UGC NAAC Re-Accredited 'A' Grade || ISO 21001:2018 (EOMS)

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मराठवाडा शिक्षण प्रसारक मंडळाचे विनायकराव पाटील महाविद्यालय, वैजापूर

यु. जी. सी. चा उत्कृष्ट गुणवत्ता क्षमता पुरस्कार प्राप्त नॅक पुनर्मूल्यांकित 'अ' श्रेणी || आय. एस. ओ. 21001:2018 (ई. ओ. एम. एस.)

Department of Mathematics *गणित विभाग*

Roger Bacon (1214-1294), an English Franciscan philosopher, scientist and scholar of the 13th century, once stated:
"Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of the world"

The department of Mathematics was established in 1968  with Mathematics as one optional subject for B.Sc.
Vision: 
To aim for quality in Mathematics that inflames students for versatile domains.
 Mission: 
To give utmost attention to the socially and economically weaker students.
To develop a student such that, when leaving college after completion of the three-year degree course, he/she is prepared with a confident frame of mind, has basic problem-solving skills, should have gained the strength to analyze something reasonable, and above all, should have established a uniform temperament.

Achievements:
    • The Department has organized one-Week Faculty Development Programme on "Recent Trends in Mathematical and Statistical Techniques and their Application in Research Methodology" in collaboration with UGC-HRDC Devi Ahilya University, Indore -July 11-16, 2022. 
    • The Department has organized one-Week Faculty Development Programme on "Applications of Mathematical Tools in Research" in collaboration with UGC-HRDC Devi Ahilya University, Indore -June 13-18, 2022
    • The Department has organized one certificate course (six-week) on “LaTeX” in 2021, one national-level faculty development program (FDP) on “LaTeX” in 2020, one national level conference on “Advances in Computational Mathematics” in 2013. The department has organized four regional level workshops for senior college teachers in the subject of Mathematics.
    • The department is a patron member of the Marathwada Mathematical Society.
    • One faculty member,  A. D. Godase received Karya Gaurav Puraskar for his dedicated service in teaching.
    • One student, Shaikh Ranisultana of class B.Sc. T. Y. got Sushiladevi Jadhav Gold medal (Medal of Merit) in the subject Mathematics in 2017-18.

 

 

HOD's Message:
The Department of Mathematics was established in 1968 with a B.Sc. degree in Mathematics. 
Department - Student Activities:
The department aims in setting goals for students to lead a balanced, successful life with proper health, good relationships, and mental peace. Also, our goal is to create a better world through education, research and extension activities.
With the constant encouragement of our staff, many of our students have participated in intercollegiate competitions in academics and won various prizes. These activities have helped the students to go for higher studies. 
Remedial classes are conducted successfully for the academic betterment of the students.
To create more interest in the subjects, students are motivated by giving more examples, diagrammatic representations, their applications in the real world using modern techniques and mathematical software packages.
Staff Activities:
At present, the department has 03 teaching staff.
The Department has organized three national-level faculty development programs (FDPs) in the academic years 2020-21 & 2021-22, one national level conference on “Advances in Computational Mathematics” in 2013. The department has organized four regional level workshops for senior college teachers in the subject of Mathematics. One certificate course on LaTeX for students is going on.
The department is a patron member of the Marathwada Mathematical Society.
 
Dr. A. D. Godase
Head of the Department of Mathematics
 
 
Dr.  A. D. Godase
(Assistant Professor & Head)
View Profile
        
                     
 
 
Prof.  R. M. Shewale
(Assistant Professor-CHB)
View Profile
 
 
 
Prof.  D. K. Sawant
(Assistant Professor-CHB)
View Profile

 

The programme offered: B.Sc. (Mathematics)
Courses offered:
F. Y. B.Sc.S. Y. B.Sc.T. Y. B.Sc.
SEMESTER-I
MAT-101
(Differential calculus)
MAT-102
(Differential equations)
SEMESTER-II
MAT-201
(Integral calculus)
MAT-202
(Analytical Geometry)
SEMESTER-III
MAT-301
(Number theory)
MAT-302
(Integral Transforms)
MAT-303
(Mechanics-I)
SEMESTER-IV
MAT-401
(Numerical analysis)
MAT-402
(Partial Differential Equations)
MAT-403
(Mechanics-II)
SEMESTER-V
MAT-501
(Real analysis-I)
MAT-502
(Abstract Algebra-I)
MAT-503
(Mathematical Statistics-I)
SEMESTER-VI
MAT-601
(Real analysis-II)
MAT-602
(Abstract Algebra-II)
MAT-603
(Mathematical Statistics-II)
  • Innovative teaching methods used: View PDF


Research Papers Published in Journal:
A. D. Godase
Sr. No.
Title with Volume & Page No.
Journal Details
Published year
Peer Review/Impact Factor
01
Recurrent formulas of the generalized Fibonacci sequences of fifth order
4(6), pp.61-67
Open
International Journal of Mathematical Archive
ISSN No. 2229-5046
2013
Refereed and Indexed Journal
02
Fundamental properties of multiplicative coupled Fibonacci sequences of fourth order under two specific schemes
4(6), pp. 74-81
Open
International Journal of Mathematical Archive
ISSN No. 2229-5046
 
2013
Refereed and Indexed Journal
03
On the properties of k- Fibonacci and k- Lucas numbers
2(1), pp. 100-106
Open
 
International Journal of Advances in Applied Mathematics and Mechanics
ISSN No. 2347-2529
2014
Refereed and Indexed Journal in Mathematical Review
04
On the properties of generalized Fibonacci like polynomials
2(3), pp. 234-251
Open
International Journal of Advances in Applied Mathematics and Mechanics
ISSN No. 2347-2529
2015
Refereed and Indexed Journal in Mathematical Review& Zentrallbath
05
On The Properties of Generalized Multiplicative Coupled Fibonacci Sequence of rth order
2(3), pp. 252-257
Open
International Journal of Advances in Applied Mathematics and Mechanics
ISSN No. 2347-2529
2015
Refereed and Indexed Journal in Mathematical Review& Zentrallbath
06
Unit Graph of Some Finite Group Zn, Cn and Dn
1(2), pp. 122-130
Open
International Journal of Universal Science and technology
ISSN No. 2454-7263
2015
Refereed and Indexed Journal
07
k Fibonacci and k Lucas Sequences and their Associated Matrices
16, pp. 43-56
Open
Journal of Tripura Mathematical Society
ISSN No. 0972-71320
2015
Refereed and Indexed Journal
08
Summation identities for k Fibonacci and k Lucas numbers using matrix methods
5(2), pp. 74-80
Open
International Journal of Mathematics and Scientific Computing
ISSN No. 2231-5330
2016
Refereed and Indexed Journal in Mathematical Review & Zentrallbath
09
Determinantal Identities for k Lucas Sequence
12, pp. 01–07
Open
Journal of New Theory
ISSN No.2149-1402
2016
Refereed and Indexed Journal
10
Fibonacci and k Lucas Sequences as Series of Fractions
04(2), pp. 107–119
Open
Mathematical Journal of Interdisciplinary Sciences
ISSN No.2278-9561
2016
Refereed and Indexed Journal in Indian Citation Index
11
Properties of k- Fibonacci Sequence Using Matrix Method
17, pp. 11–20
Open
MAYFEB Journal of Mathematics
ISSN No.2278-9561
2017
Refereed and Indexed Journal
12
Identities of Multiplicative Coupled Fibonacci Sequences of rth order.
15, pp. 48–60
Open
Journal of New Theory
ISSN No.2149-1402
 
2017
Refereed and Indexed Journal
13
Recurrent Formulas of the Generalized Fibonacci Sequences of Third & Fourth order.
17, pp. 103–110
Open
Indian Journal in Number Theory
 
2017
Refereed Journal
14
Vector Approach to a New Generalization of Fibonacci Polynomial
17, pp. 45–56
Open
Journal of New Theory
ISSN No.2149-1402
 
2017
Refereed and Indexed Journal
15
Identities Involving k-Fibonacci and k-Lucas Sequences
34(01)
pp. 125-143
Open
Mathematics Today
 0976-3228
2018
 
Refereed and Indexed Journal in ICI
16
A matrix representation of a generalized Fibonacci polynomial 
19, pp.01-19
Open
Journal of New Theory
ISSN No.2149-1402
 
2018
Refereed and Indexed Journal
17
Some Telescoping Series for k Fibonacci and k Lucas Sequences.
35(2),
pp. 44-49
Open
Mathematics Today
 0976-3228
2019
Refereed and Indexed Journal in ICI
18
Properties of k-Fibonacci and k-Lucas Octonions
50(04) ,
pp.979–998
 
Open
Indian Journal of Pure and Applied Mathematics
ISSN: 0019-5588 (print version)
ISSN: 0975-7465 (electronic version)  
2019
 
Refereed and Indexed Journal in Web of sci. & Scopus
0.516 (2019)
Impact factor
0.571 (2019)
Five year impact factor
19
Hyperbolic k- Fibonacci and k- Lucas Octonions
26(3),
pp.176-188
Open
 
Notes on Number Theory and Discrete Mathematics
1310-5132(print),
2367-8275 (online) 
2020
 
Refereed and Indexed Journal in Web of sci. & Scopus
 
0.827 (2019)
Impact factor
20
Hyperbolic k- Fibonacci and k- Lucas Quaternions
90(1-2), pp. 103-116
Open
Mathematics Student
0025-5742
 
2021
 
Refereed and Indexed Journal in Web of sci. & Scopus
0.356 (2019)
Impact factor
21
Hyperbolic k-Jacobsthal and k-Jacobsthal-Lucas Quaternions(Online first)
Open
Indian Journal of Pure and Applied Mathematics
ISSN: 0019-5588 (print version)
ISSN: 0975-7465 (electronic version)
2021
 
Refereed and Indexed Journal in Web of sci. & Scopus
0.516 (2019)
Impact factor
0.571 (2019)
Five year impact factor
22
Binomial Sums with k-Jacobsthal and k-Jacobsthal-Lucas Numbers
28(3), pp-466–476
Open
 
Notes on Number Theory and Discrete Mathematics
1310-5132(print),
2367-8275 (online)
 
2022
 
Refereed and Indexed Journal in Web of sci. & Scopus
 
 0.827 (2019)
Impact factor
Research Publications View PDF
 
Books Published:
A. D. Godase
Sr. No.
Title of the Book
No. of Pages in Book
ISSN/ISBN
Publisher
01
Advances in Computational Mathematics
166
9789380876863
Year: 2013
Educational Publishers, Aurangabad
02
Groups using Graphs
 
53
10: 1519189540
13: 978-1519189547
Year: 2015
Create Space Independent Publishing Platform by Amazon & Kindle
03
Undergraduate Course in Number Theory
68
979-8522711788
Year: 2021
Amazon Asia-Pacific
Holdings Private
Limited
04
Generalized Fibonacci Sequences
Open
195
 978-620-0-29409-8
Year: 2022
Lambert Academic Publishing. Editor: Ppetrachi

Activities:



Mentor/Mentee Details:


Slow/Advanced Learners Details:

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Faculty Activities 2016 to 2021- View

Departmental Meetings:

 

 

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Events Organised:

  • One-Week Faculty Development Programme on "Recent Trends in Mathematical and Statistical Techniques and their Application in Research Methodology" in collaboration with UGC-HRDC Devi Ahilya University, Indore -July 11-16, 2022. View Report
  • One-Week Faculty Development Programme on ''Applications of Mathematical Tools in Research'' in collaboration with UGC-HRDC Devi Ahilya University, Indore -June 13-18, 2022. View Report
  • Pi Day Quiz on 14-03-2022 View Form   View Report  View Certificates
  • National Science Day Quiz on 28-02-2022 View Form   View Report  View Certificates
  • Six-week certificate course on ''LaTeX''-November 11 to December 09, 2021.  View Brochure     View Report
  • Seven day faculty development program on ''LaTeX''-July 15-21, 2020. View Report
  • Study Tour to Saputara (Gujrat)-January 04, 2019. View Report
  • One-Day Faculty Orientation Program on “Dimensions of Curriculum, Teaching-Learning and Evaluation in Mathematics”-July 24, 2016. View Report
  • One-Day Faculty Orientation Program on “Dimensions of Curriculum, Teaching-Learning and Evaluation in Mathematics”-August 09, 2015. View Report
  • Poster Presentation Competition for Students-December 31, 2014. View Report
  • Two days, National Conference on “Advances in Computational Mathematics”-September 27-28, 2013. View Report
  • One day orientation Program in Mathematics Teaching-September 04, 2011. View Report
  • One day Workshop on “Recent Trends in Mathematics”-October 22, 2010. View Report

Student Induction Programmes:

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Teaching Videos - View PDF
Teaching Notes- View PDF
Question Banks - View PDF


 
TEACHING VIDEOS:
 
T. Y. B.Sc.
SEMESTER-6
MAT-601(Real analysis-II)
  1. Syllabus, definition of metric and metric space View
  2. Limits in metric spaces and continuous functions on metric spaces View
  3. Open sets View
  4. Closed sets View
  5. More about open sets & connected sets View
  6. Complete metric spaces View
  7. Compact metric spaces View
  8. Sets of measure zero View
  9. Upper sum and lower sum View
  10. Definition of Riemann integrable function View
  11. Properties of Riemann integrable function View
  12. Definition of Fourier series View
  13. Examples on Fourier series View

SEMESTER-5
MAT-501 (Real analysis-I)
  1. Syllabus, sets and relations View
  2. Sets and relations part-II View
  3. Functions and real valued functions-I View
  4. Functions and real valued functions-II View
  5. Maximum and minimum of real valued functions, characteristic function View
  6. Properties of characteristic function View
  7. Equivalence and countability View
  8. Examples on countable set View
  9. Real numbers, the least upper bounds View
  10. (Chapter-3 & Chapter-4) Series of real numbers and Jacobians View

MAT-502(Group theory and Ring theory)
  1. Sets, functions and integers-I View
  2. Sets, relations and integers-II View
  3. Sets, relations and integers-III View
  4. Divisibility, congruence relation, the greatest common divisor and least common multiple View

S. Y. B.Sc.
SEMESTER-4
MAT-401(Numerical analysis)
  1. Syllabus and introduction to numerical analysis View
  2. Bisection method View
  3. False position method View
  4. Problems on false position method View
  5. Newton-Raphson method View
  6. Examples on Newton-Raphson method View
  7. Generalized Newton’s method View
  8. Forward and backward differences View
  9. Forward and backward differences-II View
  10. Finite differences and relations between them View
  11. Newton’s forward and backward difference interpolation formula View
  12. Lagrange’s interpolation formula View
  13. Newtons general interpolation formula View
  14. Curve fitting (The Least square curve fitting method) View
  15. Approximation of functions (Chebyshev polynomial) View
  16. Gauss elimination and Gauss-Jordan method-I View
  17. Gauss elimination and Gauss-Jordan method-II View
  18. Method of factorization View
  19. Jacobi’s and Gauss Seidel iterative method View
  20. Eigenvalue problem View
  21. Taylor’ series method View
  22. Picard’s method View
  23. Euler’s method View
  24. Runge-Kutta method View

SEMESTER-3
MAT-301(Number theory)
  1. First principle of mathematical induction View
  2. Division Algorithm View
  3. Examples on division algorithm View
  4. Greatest common divisor View
  5. Properties of divisibility relation View
  6. (Chapter-05, Chapter-06 and Chapter-07) Chinese remainder theorem, Fermat’s theorem, number theoretic functions and Euler’s generalization of Fermat’s theorem. View

F. Y. B.Sc.
SEMESTER-1
MAT-101(Differential calculus)
Introduction to Differential calculus View
 
MAT-102(Differential equations)
Introduction to Differential equations View
SEMESTER-2
MAT-201(Integral calculus)
  1. Syllabus and Reduction formula-I View
  2. Reduction formula-2 View
  3. Reduction formula-3 View
  4. Reduction formula-4 &5 View
  5. Some important formulae View
  6. Integration of algebraic rational functions-Type-I(Non-repeated linear factors at denominator) View
  7. Integration of algebraic rational functions-Type-II(Non-repeated or repeated linear factors at denominator) View
  8. Integration of algebraic rational functions-Type-III(Linear or quadratic non-repeated factors at denominator) View
  9. Integration of Trigonometric Functions sin^nx(if n is an odd integer) View
  10. Integration of Trigonometric Functions sin^nx(if n is an even integer) View
  11. Integration of sin^nx, from 0 to pi by 2 View
  12. Integration of cos^nx (Part-1) View
  13. Integration of cos^nx (Part-2) View
  14. Integration of cos^nx (Part-3) View
  15. Integration of Cos^n(x) between 0 to Pi by 2 View
  16. Definite integral as the limit of sum View
  17. Areas of plane regions View
  18. Rectification, length of plane curves View
  19. Volumes and surfaces of revolution View
  20. Line integral, Surface integral and Volume integral View
  21. Gauss divergence theorem View
  22. Stoke’s theorem and Green’s theorem View

TEACHING NOTES:
T. Y. B.Sc.
Real analysis-I (MAT-501)
  1. Real analysis-I Download
  2. Problems in real analysis Download
  3. Lecture taken notes Download
Group theory and Ring theory (MAT-502)
  1. Corollaries to Lagranges theorem PDF
  2. Cosets  PDF
  3. Counting Principle  PDF
  4. Definition and examples of ring   PDF
  5. Homomorphism of groups   PDF
  6. Homomorphism of rings   PDF
  7. Ideals and quotient ring   PDF
  8. Isomorphisms of Groups   PDF
  9. Lagranges theorem   PDF
  10. Normal subgroups   PDF
  11. Polynomial rings   PDF
  12. Properties of ring    PDF
  13. Quotient group   PDF
Real analysis-II (MAT-601)
  1. Lecture taken notes Download
  2. Examples on Fourier series Download
  3. Lecture taken notes of Chapters 01 to 04 Download
Abstract algebra-II (MAT-602)
  1. Lecture taken notes Download
S. Y. B.Sc.
Number theory (MAT-301)
  1. Chapter 5 and 6  PDF
  2. Fermat's theorm   PDF
  3. Wilson's theorm   PDF
Numerical analysis (MAT-401)
  1. chapters-1-and-2 PDF
  2. Approximation-of-functions PDF
  3. Curve-fitting PDF
  4. Euler’s method PDF
  5. Finite-differences-and-relations-between-them PDF
  6. Gauss-elimination-and-gauss-jordan-method PDF
  7. The-eigenvalue-problem PDF
  8. Jacobi's method.  PDF
  9. Lagrange's interpolation formula  PDF
  10. Method of factorization  PDF
  11. Newton's forward and backward difference interpolation formula  PDF
  12. Newton's general interpolation formula  PDF
  13. Picard's method   PDF
  14. Taylor' series method  PDF
  15. Runge-Kutta method   PDF
  16. MAT-401 Lecture taken whiteboard notes Download
  17. MAT-401_mcqs  DOWNLOAD
F. Y. B.Sc.
Differential Calculus (MAT-101)
  1. Divergence and curl. pdf 
  2. Examples on homogeneous functions. pdf 
  3. Homogeneous functions. pdf
  4. Introduction to vectors. pdf 
  5. Partial derivatives. pdf 
     
Integral Calculus (MAT-201)
  1. Areas of plane regions  pdf 
  2. Chapters 1, 2 and 3  pdf 
  3. Definite integral as the limit of sum  pdf 
  4. Gauss divergence theorem  pdf 
  5. Important formulae  pdf 
  6. Line integral, Surface integral and Volume integral  pdf 
  7. Youtube lectures  pdf 
  8. Rectification, length of plane curves  pdf 
  9. Stoke's theorem and Green's theorem  pdf 
  10. Volumes and surfaces of revolution  pdf 

QUESTION BANK/QUIZZES:
T. Y. B.Sc.
MAT-501
  1. Sequences and Series(MAT-501)
  2. Infimum and Supremum(MAT-501)
  3. Countable sets(MAT-501)
MAT-503
  1. Introduction to Statistics(MAT-503)
  2. Statistics(MAT- 503)
  3. Probability and Statistics(MAT-503)
MAT-601
  1. Real analysis(MAT-601)
  2. Real Analysis (MAT-601)
MAT-602
  1. Abstract algebra II (MAT-602)
F. Y. B.Sc.
MAT-102
  1. Differential equations-Type, Degree & Order(MAT-102)
  2. Differential Equations(MAT-102)
MAT-201
  1. Vector Calculus(MAT-201)
  2. Integral Calculus(MAT-201)
  3. Integral Calculus (volume of the solid generated by revolution)(MAT-201)
  4. Vector Calculus Quiz II(MAT-201)
MAT-202
  1. Analytical Geometry (MAT-202)
S. Y. B.Sc.
MAT-301
  1. Number theory(MAT-301)
MAT-302
  1. Laplace Transform(MAT-302)
  2. Inverse Laplace Transform(MAT-302)

  • Data of all passed out students  of last five years  View Data
  • Data of average percentage of placement of outgoing students, average percentage of students progressing to higher education and number of students qualifying state/national/ international level examinations  during the last five years (5.2.1, 5.2.2 & 5.2.3)  View Data

 

Alumni list  of last five years-  View Data

 

  • Best Practice-I  View
  • Best Practice-II  View
Immediate Plans:
  • To make a short-term certificate course for attracting more students to B.Sc. (Mathematics) programme.
  • To organize a one-week faculty development programme for faculties and students on Mathematical Tools in Research and education.
In the next 5 Years:
  • The department has the target to produce at least five students to pass the JAM examination and will bring two research projects in the next five years.
  • To make MOOC undergraduate courses in the SWAYAM  platform for students.
In the next 10 Years:
  • To introduce M.Sc. Programme in “Mathematics”.

Six Week Online Certificate Course on “LaTeX”
Duration
Registration Opens: October 15, 2021
Registration Ends: October 30, 2021
Course Starts: November 11, 2021
Course Ends: December 09, 2021
Total Duration: 06 Weeks
This course will be conducted in a self-paced mode, i.e. all the lecture videos, slides, reading material, activities, and graded assignments will be released when the course starts. There will be recommended deadlines that you are encouraged to follow, but ultimately you have the flexibility of progressing and completing the graded assignments at your own pace. However, you will need to complete them before the course ends.
Who Should Attend
There are no prerequisites for this course, except knowledge of editing text. The course can be taken by any learner who wants to create documents using LaTeX, but especially for those who require to write articles or books, create project reports, submit papers to national/international conferences, etc.
Course Fee and Certification
There is no registration fee for the course.
Certificates will be issued on successful completion of the course based on the grading policy mentioned in the course. Please note that all certificates will be issued online. No hard copies will be given.
How to Apply
Enrollment will be strictly online, and no other mode of application will be entertained. The online registration for the course will start on 11 October 2021It will remain open till 30 October 2021.
To apply, click here or the link below:
https://forms.office.com/r/XZ4dgKYjFJ
 
Course Content
Week
Modules
Content
Duration
Files
1
Module-1
Introduction to Latex
Advantages over Microsoft Word
Various editors
The header of the LATEX document
Examples
02 Hours
PDF
Practical Assignment
01 Hour
 
Module-2
 
Typeface
Font size
Special characters
Hyphens and dots
Spacing
Examples
02 Hours
PDF
Practical Assignment
01 Hour
 
2
Module-3
 
Structure of the document class
Justification of paragraphs and sections
Examples
02 Hours
PDF
Practical Assignment
01 Hour
 
Module-4
 
Lists
Nested lists
Examples
01 Hour
PDF
Practical Assignment
01 Hour
 
3
Module-5
 
Tables
Rows spanning multiple columns
Columns spanning multiple rows
Examples
02 Hours
PDF
Practical Assignment
01 Hour
 
Module-6
 
Introduction
Image formats
Importing graphics
Wrap figure
Errors
02 Hours
PDF
Practical Assignment
01 Hour
 
4
Module-7
 
Introduction
Typesetting formulas
Equations
Examples
01 Hour
PDF
Practical Assignment
01 Hour
 
Module-8
 
Spacing
Mathematical typeface
Alignment
Labels and references
Examples and exercises
02 Hours
PDF
Practical Assignment
01 Hour
 
5
Module-9
 
Typeset lengthy equations
Matrices
Types of integral notations
Differential equations
Examples
02 Hours
PDF
Practical Assignment
01 Hour
 
Module-10
 
Mathematical accents
Binary operation symbols
Relational operators
Delimiters
Subfigures
02 Hours
PDF
Practical Assignment
01 Hour
 
6
Module-11
 
Error handling
Types of errors
Examples
01 Hour
PDF
Final Examination
01 Hour
 

Address for Communication:

Dr. A. D. Godase
Course Coordinator,
Head, Department of Mathematics,
Vinayakrao Patil Mahavidyalaya Vaijapur,
Dist. Aurangabad - 423701(MH), India
Mob: +919767046600
Email: ashokgodse2012@gmail.com
CONTACT:
Dr. A. D. Godase
Head of the Department,
Department of Mathematics,

Vinayakrao Patil Mahavidyalaya,
Vaijapur, Dist. Aurangabad – 423 701.
Tel: +91 9767046600 
ashokgodse2012@gmail.com