Department of Mathematics *गणित विभाग*
 HOME
 HOD's DESK
 FACULTY
 COURSES OFFERED
 SYLLABUS
 POs, PSOs & COs
 RESEARCH ACTIVITIES
 STUDENT PROFILE
 TIME TABLE
 RESULTS
 STUDENT ACTIVITIES
 FACULTY ACTIVITIES
 EVENTS
 econtent
 PLACEMENTS
 ALUMNI DETAILS
 BEST PRACTICES
 FUTURE PLANS
 Certificate course on “LaTeX”
Roger Bacon (12141294), 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 threeyear degree course, he/she is prepared with a confident frame of mind, has basic problemsolving skills, should have gained the strength to analyze something reasonable, and above all, should have established a uniform temperament.
Achievements:
The Department has organized oneWeek Faculty Development Programme on "Recent Trends in Mathematical and Statistical Techniques and their Application in Research Methodology" in collaboration with UGCHRDC Devi Ahilya University, Indore July 1116, 2022.
The Department has organized oneWeek Faculty Development Programme on "Applications of Mathematical Tools in Research" in collaboration with UGCHRDC Devi Ahilya University, Indore June 1318, 2022
The Department has organized one certificate course (sixweek) on “LaTeX” in 2021, one nationallevel 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 201718.
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 nationallevel faculty development programs (FDPs) in the academic years 202021 & 202122, 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 ProfessorCHB)
View Profile
Prof. S. S. Jadhav
(Assistant ProfessorCHB)
View Profile
The programme offered: B.Sc. (Mathematics)
Courses offered:
F. Y. B.Sc.  S. Y. B.Sc.  T. Y. B.Sc. 
SEMESTERIMAT101(Analytical Geometry)MAT102(Differential calculus)SEMESTERIIMAT201(Number theory)MAT202(Integral calculus)  SEMESTERIIICore Courses(DSC1C)MAT301(Differential Equations)MAT302(Laplace and Fourier Transforms)MAT302P(Lab courseIBased on MAT301 & MAT302)Elective CourseSEC1(Any one)MAT303(MechanicsI)MAT304(Graph Theory)SEMESTERIVCore Courses(DSC1C)MAT401(Partial Differential Equations)MAT402(Numerical Analysis)MAT402P(Lab courseIIBased on MAT401 & MAT402)Elective CourseSEC1(Any one)MAT403(MechanicsII)MAT404(Complex Analysis)  SEMESTERVMAT501(Real analysisI)MAT502(Abstract AlgebraI)MAT503(Mathematical StatisticsI)SEMESTERVIMAT601(Real analysisII)MAT602(Abstract AlgebraII)MAT603(Mathematical StatisticsII) 
Choice Based Credit and Grading System Rules, Regulation and Structure for B. Sc. Courses View PDF
B.Sc. Firstyear Restructured Syllabus with effect from the academic year 202223 View PDF
B.Sc. Secondyear Restructured Syllabus with effect from the academic year 202324 View PDF
B.Sc. Thirdyear Restructured Syllabus with effect from the academic year 201516 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.6167Open  International Journal of Mathematical ArchiveISSN No. 22295046  2013  Refereed and Indexed Journal 
02  Fundamental properties of multiplicative coupled Fibonacci sequences of fourth order under two specific schemes4(6), pp. 7481Open  International Journal of Mathematical ArchiveISSN No. 22295046  2013  Refereed and Indexed Journal 
03  On the properties of k Fibonacci and k Lucas numbers2(1), pp. 100106Open  International Journal of Advances in Applied Mathematics and MechanicsISSN No. 23472529  2014  Refereed and Indexed Journal in Mathematical Review 
04  On the properties of generalized Fibonacci like polynomials2(3), pp. 234251Open  International Journal of Advances in Applied Mathematics and MechanicsISSN No. 23472529  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. 252257Open  International Journal of Advances in Applied Mathematics and MechanicsISSN No. 23472529  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. 122130Open  International Journal of Universal Science and technologyISSN No. 24547263  2015  Refereed and Indexed Journal 
07  k Fibonacci and k Lucas Sequences and their Associated Matrices16, pp. 4356Open  Journal of Tripura Mathematical SocietyISSN No. 097271320  2015  Refereed and Indexed Journal 
08  Summation identities for k Fibonacci and k Lucas numbers using matrix methods5(2), pp. 7480Open  International Journal of Mathematics and Scientific ComputingISSN No. 22315330  2016  Refereed and Indexed Journal in Mathematical Review & Zentrallbath 
09  Determinantal Identities for k Lucas Sequence12, pp. 01–07Open  Journal of New TheoryISSN No.21491402  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.22789561  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.22789561  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.21491402  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.21491402  2017  Refereed and Indexed Journal 
15  Identities Involving kFibonacci and kLucas Sequences34(01)pp. 125143Open  Mathematics Today09763228  2018  Refereed and Indexed Journal in ICI 
16  A matrix representation of a generalized Fibonacci polynomial19, pp.0119Open  Journal of New TheoryISSN No.21491402  2018  Refereed and Indexed Journal 
17  Some Telescoping Series for k Fibonacci and k Lucas Sequences.35(2),pp. 4449Open  Mathematics Today09763228  2019  Refereed and Indexed Journal in ICI 
18  Properties of kFibonacci and kLucas Octonions50(04) ,pp.979–998Open  Indian Journal of Pure and Applied MathematicsISSN: 00195588 (print version)ISSN: 09757465 (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.176188Open  Notes on Number Theory and Discrete Mathematics13105132(print),23678275 (online)  2020  Refereed and Indexed Journal in Web of sci. & Scopus0.827 (2019)Impact factor 
20  Hyperbolic k Fibonacci and k Lucas Quaternions90(12), pp. 103116Open  Mathematics Student00255742  2021  Refereed and Indexed Journal in Web of sci. & Scopus0.356 (2019)Impact factor 
21  Hyperbolic kJacobsthal and kJacobsthalLucas Quaternions(Online first)Open  Indian Journal of Pure and Applied MathematicsISSN: 00195588 (print version)ISSN: 09757465 (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 kJacobsthal and kJacobsthalLucas Numbers28(3), pp466–476Open  Notes on Number Theory and Discrete Mathematics13105132(print),23678275 (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: 9781519189547Year: 2015  Create Space Independent Publishing Platform by Amazon & Kindle 
03  Undergraduate Course in Number Theory  68  9798522711788Year: 2021  Amazon AsiaPacificHoldings PrivateLimited 
04  Generalized Fibonacci SequencesOpen  195  9786200294098Year: 2022  Lambert Academic Publishing. Editor: Ppetrachi 
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 MuseumGujrat 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.
Twentysix 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 201617 View PDF
 Academic year 201718 View PDF
 Academic year 201819 View PDF
 Academic year 201920 View PDF
 Academic year 202021 View PDF
Slow/Advanced Learners Details:
 Academic year 201617 View PDF
 Academic year 201718 View PDF
 Academic year 201819 View PDF
 Academic year 201920 View PDF
 Academic year 202021 View PDF
⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗
Faculty Activities 2016 to 2021 View
Departmental Meetings:
Academic year 201617 View PDF
Academic year 201718 View PDF
Academic year 201819 View PDF
Academic year 201920 View PDF
Academic year 202021 View PDF
⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗
Events organized:

National Quiz Competition in Mathematics on the occasion of Fibonacci Day2023 (23112023) List of successsful Participants View Form View Report View Certificates

National Science Day Quiz on 28022023 View Form View Report View Certificates

National Quiz Competition in Mathematics on the occasion of National Mathematics Day2022 (22122022) View Brochure View Form View Report View Certificates

OneWeek Faculty Development Program on "Recent Trends in Mathematical and Statistical Techniques and their Application in Research Methodology" in collaboration with UGCHRDC Devi Ahilya University, Indore July 1116, 2022. View Report

OneWeek Faculty Development Program on ''Applications of Mathematical Tools in Research'' in collaboration with UGCHRDC Devi Ahilya University, Indore June 1318, 2022. View Report

Pi Day Quiz on 14032022 View Form View Report View Certificates

National Science Day Quiz on 28022022 View Form View Report View Certificates

Sixweek certificate course on ''LaTeX''November 11 to December 09, 2021. View Brochure View Report

Sevenday faculty development program on ''LaTeX''July 1521, 2020. View Report

Study Tour to Saputara (Gujrat)January 04, 2019. View Report

OneDay Faculty Orientation Program on “Dimensions of Curriculum, TeachingLearning and Evaluation in Mathematics”July 24, 2016. View Report

OneDay Faculty Orientation Program on “Dimensions of Curriculum, TeachingLearning and Evaluation in Mathematics”August 09, 2015. View Report

Poster Presentation Competition for StudentsDecember 31, 2014. View Report

Two days, National Conference on “Advances in Computational Mathematics”September 2728, 2013. View Report

One day orientation program in Mathematics TeachingSeptember 04, 2011. View Report

Oneday Workshop on “Recent Trends in Mathematics”October 22, 2010. View Report
Student Induction Programs:

Academic year 201617 View PDF

Academic year 201718 View PDF

Academic year 201819 View PDF

Academic year 201920 View PDF

Academic year 202021 View PDF
⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗⊗
Teaching Videos  View PDF
Teaching Notes View PDF
Question Banks  View PDF
TEACHING VIDEOS:
T. Y. B.Sc.
SEMESTER6
MAT601(Real analysisII)
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
SEMESTER5
MAT501 (Real analysisI)
Syllabus, sets and relations View
Sets and relations partII View
Functions and real valued functionsI View
Functions and real valued functionsII 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
(Chapter3 & Chapter4) Series of real numbers and Jacobians View
MAT502(Group theory and Ring theory)
Sets, functions and integersI View
Sets, relations and integersII View
Sets, relations and integersIII View
Divisibility, congruence relation, the greatest common divisor and least common multiple View
S. Y. B.Sc.
SEMESTER4
MAT401(Numerical analysis)
Syllabus and introduction to numerical analysis View
Bisection method View
False position method View
Problems on false position method View
NewtonRaphson method View
Examples on NewtonRaphson method View
Generalized Newton’s method View
Forward and backward differences View
Forward and backward differencesII 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 GaussJordan methodI View
Gauss elimination and GaussJordan methodII 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
RungeKutta method View
SEMESTER3
MAT301(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
(Chapter05, Chapter06 and Chapter07) Chinese remainder theorem, Fermat’s theorem, number theoretic functions and Euler’s generalization of Fermat’s theorem. View
F. Y. B.Sc.
SEMESTER1
MAT101(Differential calculus)
Introduction to Differential calculus View
MAT102(Differential equations)
Introduction to Differential equations View
SEMESTER2
MAT201(Integral calculus)
Syllabus and Reduction formulaI View
Reduction formula2 View
Reduction formula3 View
Reduction formula4 &5 View
Some important formulae View
Integration of algebraic rational functionsTypeI(Nonrepeated linear factors at denominator) View
Integration of algebraic rational functionsTypeII(Nonrepeated or repeated linear factors at denominator) View
Integration of algebraic rational functionsTypeIII(Linear or quadratic nonrepeated 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 (Part1) View
Integration of cos^nx (Part2) View
Integration of cos^nx (Part3) 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 analysisI (MAT501)
Group theory and Ring theory (MAT502)
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 analysisII (MAT601)
Lecture taken notes Download
Examples on Fourier series Download
Lecture taken notes of Chapters 01 to 04 Download
Abstract algebraII (MAT602)
Lecture taken notes Download
S. Y. B.Sc.
Number theory (MAT301)
Numerical analysis (MAT401)
chapters1and2 PDF
Approximationoffunctions PDF
Curvefitting PDF
Euler’s method PDF
Finitedifferencesandrelationsbetweenthem PDF
Gausseliminationandgaussjordanmethod PDF
Theeigenvalueproblem 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
RungeKutta method PDF
MAT401 Lecture taken whiteboard notes Download
MAT401_mcqs DOWNLOAD
F. Y. B.Sc.
Differential Calculus (MAT101)
Divergence and curl. pdf
Examples on homogeneous functions. pdf
Homogeneous functions. pdf
Introduction to vectors. pdf
Partial derivatives. pdf
Integral Calculus (MAT201)
Vector calculusChapter01 Download
Vector calculusChapter02 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.
MAT501
MAT503
MAT601
MAT602
F. Y. B.Sc.
MAT102
MAT201
Vector Calculus(MAT201)
Integral Calculus(MAT201)
Integral Calculus (volume of the solid generated by revolution)(MAT201)
Vector Calculus Quiz II(MAT201)
MAT202
S. Y. B.Sc.
MAT301
MAT302
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 shortterm certificate course for attracting more students to B.Sc. (Mathematics) programme.
To organize a oneweek 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 Certificate Course on “LaTeX”
Duration
Registrations Opens: January 15, 2023
Registrations Ends: March 15, 2023
Course Starts: April 15, 2023
Course Ends: May 31, 2023
Total Duration: 06 Weeks
This course will be conducted in a selfpaced 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 writing 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 15 January 2023. It will remain open till 15 March 2023.
To apply, click here or the link below:
https://forms.office.com/r/XVVvuchNLi
Course Content
Week  Modules  Content  Duration  Files 
1  Module1  Introduction to LatexAdvantages over Microsoft WordVarious editorsThe header of the LATEX documentExamples  02 Hours  
Practical Assignment  01 Hour  
Module2  TypefaceFont sizeSpecial charactersHyphens and dotsSpacingExamples  02 Hours  
Practical Assignment  01 Hour  
2  Module3  Structure of the document classJustification of paragraphs and sectionsExamples  02 Hours  
Practical Assignment  01 Hour  
Module4  ListsNested listsExamples  01 Hour  
Practical Assignment  01 Hour  
3  Module5  TablesRows spanning multiple columnsColumns spanning multiple rowsExamples  02 Hours  
Practical Assignment  01 Hour  
Module6  IntroductionImage formatsImporting graphicsWrap figureErrors  02 Hours  
Practical Assignment  01 Hour  
4  Module7  IntroductionTypesetting formulasEquationsExamples  01 Hour  
Practical Assignment  01 Hour  
Module8  SpacingMathematical typefaceAlignmentLabels and referencesExamples and exercises  02 Hours  
Practical Assignment  01 Hour  
5  Module9  Typeset lengthy equationsMatricesTypes of integral notationsDifferential equationsExamples  02 Hours  
Practical Assignment  01 Hour  
Module10  Mathematical accentsBinary operation symbolsRelational operatorsDelimitersSubfigures  02 Hours  
Practical Assignment  01 Hour  
6  Module11  Error handlingTypes of errorsExamples  01 Hour  
Final Examination  01 Hour 