Department of Mathematics *गणित विभाग*
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- Certificate course on “LaTeX”
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-IMAT-101(Differential calculus)MAT-102(Differential equations)SEMESTER-IIMAT-201(Integral calculus)MAT-202(Analytical Geometry) | SEMESTER-IIIMAT-301(Number theory)MAT-302(Integral Transforms)MAT-303(Mechanics-I)SEMESTER-IVMAT-401(Numerical analysis)MAT-402(Partial Differential Equations)MAT-403(Mechanics-II) | SEMESTER-VMAT-501(Real analysis-I)MAT-502(Abstract Algebra-I)MAT-503(Mathematical Statistics-I)SEMESTER-VIMAT-601(Real analysis-II)MAT-602(Abstract Algebra-II)MAT-603(Mathematical Statistics-II) |
Choice Based Credit and Grading System Rules, Regulation and Structure for B. Sc. Courses View PDF
B.Sc. First-year Restructured Syllabus with effect from the academic year 2022-23 View PDF
B.Sc. Second-year Restructured Syllabus with effect from the academic year 2014-15 View PDF
B.Sc. Third-year Restructured Syllabus with effect from the academic year 2015-16 View PDF
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 order4(6), pp.61-67Open | International Journal of Mathematical ArchiveISSN No. 2229-5046 | 2013 | Refereed and Indexed Journal |
02 | Fundamental properties of multiplicative coupled Fibonacci sequences of fourth order under two specific schemes4(6), pp. 74-81Open | International Journal of Mathematical ArchiveISSN No. 2229-5046 | 2013 | Refereed and Indexed Journal |
03 | On the properties of k- Fibonacci and k- Lucas numbers2(1), pp. 100-106Open | International Journal of Advances in Applied Mathematics and MechanicsISSN No. 2347-2529 | 2014 | Refereed and Indexed Journal in Mathematical Review |
04 | On the properties of generalized Fibonacci like polynomials2(3), pp. 234-251Open | International Journal of Advances in Applied Mathematics and MechanicsISSN No. 2347-2529 | 2015 | Refereed and Indexed Journal in Mathematical Review& Zentrallbath |
05 | On The Properties of Generalized Multiplicative Coupled Fibonacci Sequence of r^{th} order2(3), pp. 252-257Open | International Journal of Advances in Applied Mathematics and MechanicsISSN No. 2347-2529 | 2015 | Refereed and Indexed Journal in Mathematical Review& Zentrallbath |
06 | Unit Graph of Some Finite Group Z_{n}, C_{n }and D_{n}1(2), pp. 122-130Open | International Journal of Universal Science and technologyISSN No. 2454-7263 | 2015 | Refereed and Indexed Journal |
07 | k Fibonacci and k Lucas Sequences and their Associated Matrices16, pp. 43-56Open | Journal of Tripura Mathematical SocietyISSN No. 0972-71320 | 2015 | Refereed and Indexed Journal |
08 | Summation identities for k Fibonacci and k Lucas numbers using matrix methods5(2), pp. 74-80Open | International Journal of Mathematics and Scientific ComputingISSN No. 2231-5330 | 2016 | Refereed and Indexed Journal in Mathematical Review & Zentrallbath |
09 | Determinantal Identities for k Lucas Sequence12, pp. 01–07Open | Journal of New TheoryISSN No.2149-1402 | 2016 | Refereed and Indexed Journal |
10 | Fibonacci and k Lucas Sequences as Series of Fractions04(2), pp. 107–119Open | Mathematical Journal of Interdisciplinary SciencesISSN No.2278-9561 | 2016 | Refereed and Indexed Journal in Indian Citation Index |
11 | Properties of k- Fibonacci Sequence Using Matrix Method17, pp. 11–20Open | MAYFEB Journal of MathematicsISSN No.2278-9561 | 2017 | Refereed and Indexed Journal |
12 | Identities of Multiplicative Coupled Fibonacci Sequences of r^{th} order.15, pp. 48–60Open | Journal of New TheoryISSN No.2149-1402 | 2017 | Refereed and Indexed Journal |
13 | Recurrent Formulas of the Generalized Fibonacci Sequences of Third & Fourth order.17, pp. 103–110Open | Indian Journal in Number Theory | 2017 | Refereed Journal |
14 | Vector Approach to a New Generalization of Fibonacci Polynomial17, pp. 45–56Open | Journal of New TheoryISSN No.2149-1402 | 2017 | Refereed and Indexed Journal |
15 | Identities Involving k-Fibonacci and k-Lucas Sequences34(01)pp. 125-143Open | Mathematics Today0976-3228 | 2018 | Refereed and Indexed Journal in ICI |
16 | A matrix representation of a generalized Fibonacci polynomial19, pp.01-19Open | Journal of New TheoryISSN No.2149-1402 | 2018 | Refereed and Indexed Journal |
17 | Some Telescoping Series for k Fibonacci and k Lucas Sequences.35(2),pp. 44-49Open | Mathematics Today0976-3228 | 2019 | Refereed and Indexed Journal in ICI |
18 | Properties of k-Fibonacci and k-Lucas Octonions50(04) ,pp.979–998Open | Indian Journal of Pure and Applied MathematicsISSN: 0019-5588 (print version)ISSN: 0975-7465 (electronic version) | 2019 | Refereed and Indexed Journal in Web of sci. & Scopus0.516 (2019)Impact factor0.571 (2019)Five year impact factor |
19 | Hyperbolic k- Fibonacci and k- Lucas Octonions26(3),pp.176-188Open | Notes on Number Theory and Discrete Mathematics1310-5132(print),2367-8275 (online) | 2020 | Refereed and Indexed Journal in Web of sci. & Scopus0.827 (2019)Impact factor |
20 | Hyperbolic k- Fibonacci and k- Lucas Quaternions90(1-2), pp. 103-116Open | Mathematics Student0025-5742 | 2021 | Refereed and Indexed Journal in Web of sci. & Scopus0.356 (2019)Impact factor |
21 | Hyperbolic k-Jacobsthal and k-Jacobsthal-Lucas Quaternions(Online first)Open | Indian Journal of Pure and Applied MathematicsISSN: 0019-5588 (print version)ISSN: 0975-7465 (electronic version) | 2021 | Refereed and Indexed Journal in Web of sci. & Scopus0.516 (2019)Impact factor0.571 (2019)Five year impact factor |
22 | Binomial Sums with k-Jacobsthal and k-Jacobsthal-Lucas Numbers28(3), pp-466–476Open | Notes on Number Theory and Discrete Mathematics1310-5132(print),2367-8275 (online) | 2022 | Refereed and Indexed Journal in Web of sci. & Scopus0.827 (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 | 9789380876863Year: 2013 | Educational Publishers, Aurangabad |
02 | Groups using Graphs | 53 | 10: 151918954013: 978-1519189547Year: 2015 | Create Space Independent Publishing Platform by Amazon & Kindle |
03 | Undergraduate Course in Number Theory | 68 | 979-8522711788Year: 2021 | Amazon Asia-PacificHoldings PrivateLimited |
04 | Generalized Fibonacci SequencesOpen | 195 | 978-620-0-29409-8Year: 2022 | Lambert Academic Publishing. Editor: Ppetrachi |
- Student List 2016-17
- Student List 2017-18
- Student List 2018-19
- Student List 2019-20
- Student List 2020-21
- Student List 2021-22
Activities:
Two students participated in the 20th Annual Seminar Competition for UG/PG Students organized by Government Engineering College, Aurangabad, sponsored by Marathwada Mathematical Society, Aurangabad on 03rd February 03, 2020.
Study Tour to Saputara Museum-Gujrat on January 04, 2020.
Two students participated in the 19th annual Seminar Competition for UG/PG students organized at S. B. Science College, Aurangabad, sponsored by Marathwada Mathematical Society, Aurangabad on February 01, 2019.
Nine students participated in the 06th Ramanujan Quiz Competition for UG/PG students organized by S. B. College, Aurangabad in collaboration with Marathwada Mathematical Society, Aurangabad on January 13, 2019.
One student participated in the18th Annual Seminar Competition for UG/PG Students organized by Rafique Zhakeria College, Aurangabad & Marathwada Mathematical Society, Aurangabad on February 01, 2018.
Twenty-six students participated in the 05th Ramanujan Quiz Competition for UG/PG students organized by S. B. College, Aurangabad in collaboration with Marathwada Mathematical Society, Aurangabad on January 21, 2018.
Two students participated in the 17th Annual Seminar Competition for UG/PG Students organized by Vivekanand College, Aurangabad & Marathwada Mathematical Society, Aurangabad on January 27 & 28, 2016.
Twenty students participated in the 04th Ramanujan Quiz Competition for UG/PG students organized by S. B. College, Aurangabad in collaboration with Marathwada Mathematical Society, Aurangabad on January 22, 2017.
The poster presentation competition was organized for undergraduate students on December 31, 2014.
Mentor/Mentee Details:
- Academic year 2016-17 View PDF
- Academic year 2017-18 View PDF
- Academic year 2018-19 View PDF
- Academic year 2019-20 View PDF
- Academic year 2020-21 View PDF
Slow/Advanced Learners Details:
- Academic year 2016-17 View PDF
- Academic year 2017-18 View PDF
- Academic year 2018-19 View PDF
- Academic year 2019-20 View PDF
- Academic year 2020-21 View PDF
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Faculty Activities 2016 to 2021- View
Departmental Meetings:
Academic year 2016-17 View PDF
Academic year 2017-18 View PDF
Academic year 2018-19 View PDF
Academic year 2019-20 View PDF
Academic year 2020-21 View PDF
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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:
Academic year 2016-17 View PDF
Academic year 2017-18 View PDF
Academic year 2018-19 View PDF
Academic year 2019-20 View PDF
Academic year 2020-21 View PDF
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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)
Syllabus, definition of metric and metric space View
Limits in metric spaces and continuous functions on metric spaces View
Open sets View
Closed sets View
More about open sets & connected sets View
Complete metric spaces View
Compact metric spaces View
Sets of measure zero View
Upper sum and lower sum View
Definition of Riemann integrable function View
Properties of Riemann integrable function View
Definition of Fourier series View
Examples on Fourier series View
SEMESTER-5
MAT-501 (Real analysis-I)
Syllabus, sets and relations View
Sets and relations part-II View
Functions and real valued functions-I View
Functions and real valued functions-II View
Maximum and minimum of real valued functions, characteristic function View
Properties of characteristic function View
Equivalence and countability View
Examples on countable set View
Real numbers, the least upper bounds View
(Chapter-3 & Chapter-4) Series of real numbers and Jacobians View
MAT-502(Group theory and Ring theory)
Sets, functions and integers-I View
Sets, relations and integers-II View
Sets, relations and integers-III View
Divisibility, congruence relation, the greatest common divisor and least common multiple View
S. Y. B.Sc.
SEMESTER-4
MAT-401(Numerical analysis)
Syllabus and introduction to numerical analysis View
Bisection method View
False position method View
Problems on false position method View
Newton-Raphson method View
Examples on Newton-Raphson method View
Generalized Newton’s method View
Forward and backward differences View
Forward and backward differences-II View
Finite differences and relations between them View
Newton’s forward and backward difference interpolation formula View
Lagrange’s interpolation formula View
Newtons general interpolation formula View
Curve fitting (The Least square curve fitting method) View
Approximation of functions (Chebyshev polynomial) View
Gauss elimination and Gauss-Jordan method-I View
Gauss elimination and Gauss-Jordan method-II View
Method of factorization View
Jacobi’s and Gauss Seidel iterative method View
Eigenvalue problem View
Taylor’ series method View
Picard’s method View
Euler’s method View
Runge-Kutta method View
SEMESTER-3
MAT-301(Number theory)
First principle of mathematical induction View
Division Algorithm View
Examples on division algorithm View
Greatest common divisor View
Properties of divisibility relation View
(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)
Syllabus and Reduction formula-I View
Reduction formula-2 View
Reduction formula-3 View
Reduction formula-4 &5 View
Some important formulae View
Integration of algebraic rational functions-Type-I(Non-repeated linear factors at denominator) View
Integration of algebraic rational functions-Type-II(Non-repeated or repeated linear factors at denominator) View
Integration of algebraic rational functions-Type-III(Linear or quadratic non-repeated factors at denominator) View
Integration of Trigonometric Functions sin^nx(if n is an odd integer) View
Integration of Trigonometric Functions sin^nx(if n is an even integer) View
Integration of sin^nx, from 0 to pi by 2 View
Integration of cos^nx (Part-1) View
Integration of cos^nx (Part-2) View
Integration of cos^nx (Part-3) View
Integration of Cos^n(x) between 0 to Pi by 2 View
Definite integral as the limit of sum View
Areas of plane regions View
Rectification, length of plane curves View
Volumes and surfaces of revolution View
Line integral, Surface integral and Volume integral View
Gauss divergence theorem View
Stoke’s theorem and Green’s theorem View
TEACHING NOTES:
T. Y. B.Sc.
Real analysis-I (MAT-501)
Group theory and Ring theory (MAT-502)
Corollaries to Lagranges theorem PDF
Cosets PDF
Counting Principle PDF
Definition and examples of ring PDF
Homomorphism of groups PDF
Homomorphism of rings PDF
Ideals and quotient ring PDF
Isomorphisms of Groups PDF
Lagranges theorem PDF
Normal subgroups PDF
Polynomial rings PDF
Properties of ring PDF
Quotient group PDF
Real analysis-II (MAT-601)
Lecture taken notes Download
Examples on Fourier series Download
Lecture taken notes of Chapters 01 to 04 Download
Abstract algebra-II (MAT-602)
Lecture taken notes Download
S. Y. B.Sc.
Number theory (MAT-301)
Numerical analysis (MAT-401)
chapters-1-and-2 PDF
Approximation-of-functions PDF
Curve-fitting PDF
Euler’s method PDF
Finite-differences-and-relations-between-them PDF
Gauss-elimination-and-gauss-jordan-method PDF
The-eigenvalue-problem PDF
Jacobi's method. PDF
Lagrange's interpolation formula PDF
Method of factorization PDF
Newton's forward and backward difference interpolation formula PDF
Newton's general interpolation formula PDF
Picard's method PDF
Taylor' series method PDF
Runge-Kutta method PDF
MAT-401 Lecture taken whiteboard notes Download
MAT-401_mcqs DOWNLOAD
F. Y. B.Sc.
Differential Calculus (MAT-101)
Divergence and curl. pdf
Examples on homogeneous functions. pdf
Homogeneous functions. pdf
Introduction to vectors. pdf
Partial derivatives. pdf
Integral Calculus (MAT-201)
Vector calculus-Chapter-01 Download
Vector calculus-Chapter-02 Download
Online lecture taken notes Download
Areas of plane regions pdf
Chapters 1, 2 and 3 pdf
Definite integral as the limit of sum pdf
Gauss divergence theorem pdf
Important formulae pdf
Line integral, Surface integral and Volume integral pdf
Youtube lectures pdf
Rectification, length of plane curves pdf
Stoke's theorem and Green's theorem pdf
Volumes and surfaces of revolution pdf
QUESTION BANK/QUIZZES:
T. Y. B.Sc.
MAT-501
MAT-503
MAT-601
MAT-602
F. Y. B.Sc.
MAT-102
MAT-201
Vector Calculus(MAT-201)
Integral Calculus(MAT-201)
Integral Calculus (volume of the solid generated by revolution)(MAT-201)
Vector Calculus Quiz II(MAT-201)
MAT-202
S. Y. B.Sc.
MAT-301
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
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 2021. It 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 LatexAdvantages over Microsoft WordVarious editorsThe header of the LATEX documentExamples | 02 Hours | |
Practical Assignment | 01 Hour | |||
Module-2 | TypefaceFont sizeSpecial charactersHyphens and dotsSpacingExamples | 02 Hours | ||
Practical Assignment | 01 Hour | |||
2 | Module-3 | Structure of the document classJustification of paragraphs and sectionsExamples | 02 Hours | |
Practical Assignment | 01 Hour | |||
Module-4 | ListsNested listsExamples | 01 Hour | ||
Practical Assignment | 01 Hour | |||
3 | Module-5 | TablesRows spanning multiple columnsColumns spanning multiple rowsExamples | 02 Hours | |
Practical Assignment | 01 Hour | |||
Module-6 | IntroductionImage formatsImporting graphicsWrap figureErrors | 02 Hours | ||
Practical Assignment | 01 Hour | |||
4 | Module-7 | IntroductionTypesetting formulasEquationsExamples | 01 Hour | |
Practical Assignment | 01 Hour | |||
Module-8 | SpacingMathematical typefaceAlignmentLabels and referencesExamples and exercises | 02 Hours | ||
Practical Assignment | 01 Hour | |||
5 | Module-9 | Typeset lengthy equationsMatricesTypes of integral notationsDifferential equationsExamples | 02 Hours | |
Practical Assignment | 01 Hour | |||
Module-10 | Mathematical accentsBinary operation symbolsRelational operatorsDelimitersSubfigures | 02 Hours | ||
Practical Assignment | 01 Hour | |||
6 | Module-11 | Error handlingTypes of errorsExamples | 01 Hour | |
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
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