MLACW (now mLAC) is an institution of excellence located strategically in the vicinity of national institutes of repute, such as Indian Institute of Science, Institute of Wood Science & Technology, National Institute of Advanced Studies, Raman Research Institute and Central Power Research Institute.

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About

Department of Mathematics

Our Mission

To enable students 

  • To develop interest in mathematics. 
  • To have a thorough understanding of the mathematical concepts.
  • Then to apply them practically using FOSS tools.
  • To score well in their university examinations which enable them to pursue their higher studies. 

Vision

  • Large number of students should volunteer to opt for learning mathematics at higher level.
  • To introduce ADD ON course to support mathematical lab using FOSS tools.
  • To motivate students for higher education and research culture in mathematics.
  • To introduce PG and research.
  • To introduce project work, internship in consultation with leading industries

Department of Mathematics

1. History of the Department

• Mathematics Department was established in 1975 by Prof. Srirangamma.

• Prof. J. V. Sandhya joined the department in July 1977 and was the HOD from 1977 to January 2009.

• Prof. R. Chayadevi joined the department in August 1977 and was the HOD from Feb 2009 to Oct 2015.

• Dr. Nanda Kulkarni is the present Head of the Department.

2. Key milestones of the department

• Introduction of practical in Mathematics using FOSS tools for the students pursuing UG course in the year 2014 for better understanding of mathematical concepts and developing soft skills for designing and developing programs.

• From 2016 – Is participant under DBT funded star status.

• In the year 2016-17 20 (out of 70) students joined M.Sc in Mathematics at Bangalore University.

• In the year 2017-2018 14 (out of 76) students joined M.Sc in Mathematics at Bangalore University.

• In the year 2017-2018 Introduction of R- software for doing statistical calculations and Geogebra for visualisation of mathematics concepts.

• In the year 2018-2019, first autonomous batch of students graduated with 17(out of 67) students joining M.Sc in Mathematics at Bangalore University and various autonomous colleges.

Achievements for the year 2019 - 2020

A. Dr. Nanda Kulkarni

I. Academic Consultancy

1. Officially invited by the DCE- Directorate of Collegiate Education to present the scheme of valuation of B.Sc. Paper III Mathematics for Video recording on 2nd Nov by Edustat satellite which has been uploaded in YouTube.

2. Included is a committee of 6 members as subject experts to arrange for the virtual class for even semester, syllabus of B.Sc. Mathematics, This meeting was held in Director office on 14th Nov 2019, at the Directorate of Collegiate Education, Bangalore.

B. Narayani R Shankar

I. Papers Published

1. B. Sooryanarayana, Narayani R Shankar, Yogalakshmi S., Radio number of k th-transformation graphs of a Path, International Journal of Applied Graph Theory, Vol. 3, No.2 (2019), 39 – 62. ISSN(Online): 2456 – 7884

II. Joined Ph.D. programme in Mathematics, under VTU in February, 2020.

III. Completed Vidwat Final Exam in Bharathanatyam Dance conducted by KSEEB in June 2019.

C. Lakshmi B N

I. Papers Presented

1. Titled “Homotopy continuation method to solve system of nonlinear equations” in 43rd ISSC, jointly organized by BCU and Indian Social Science Academy, Bangalore, from 17th to 21st January, 2020.

II. Joined Ph.D. programme in Mathematics, under BCU in January, 2020.

D. Ranjitha D J - Pursuing B.Ed. under Tumkur University.

E. Shylaja G - Papers presented

1. Titled " A new finite element method using MATLAB for Poisson's equation in axisymmetric domain" in the International virtual conference on Bridging innovative trends in Mathematics, Engineering & Technology, organized by BAIT college, Tamilnadu, from 18th to 19th December 2020.

II. Pursuing Ph.D. in Amrita Vishwa Vidyapeetham, Bengaluru Campus.

  • Future Plans for the academic year 2018-2019
  1.  To introduce Post Graduate courses. 
  2. To encourage research culture among students. 
  3. To introduce project work, internship in consultation with leading industries provided the Autonomy is given for selection of topics. 
  • Futures Plans for the academic year 2019-2020
  1. Introduction of M.Sc. course and research center in Mathematics. 
  2. Equipping staff to teach Post graduation through books, journals, latest math software. 
  3.  To get major and minor projects funded by UGC or other organization. 
  4. Conduct summer classes for school students to bring about awareness of mathematical software. 
  5. Encouraging students to make mathematical models to cultivate creativity. 
  • Future Plans for the academic year 2019-2020
  1. To conduct seminars and conferences in collaboration with leading organizations
  2. To motivate students to pursue higher studies
  3. To arrange seminars by eminent mathematicians
  4. To organize talks by industrial experts
  5.  Arranging Industrial visits. 
  6. Guiding students to present and publish papers.
  7.  Creating awareness for students to find opportunities for internships, highlighting the Industrial requirements leading to employment.
  8. To give awareness and information of various courses after their graduation in advance to help them to prepare for the same.
  9. To encourage the students to apply for summer fellowships in premier institutions
  • Best practices of 2018-2019
  1. Information of the details is given to apply for post graduation in mathematics. Information regarding the course, entrance exams, course structure for colleges in and around Bangalore 
  2. Training for fast learners and other interested students for post graduate entrance exams. 
  3. Motivating and training students to tackle aptitude tests in campus placements. 
  4. Encourage students to use the department library to study and develop an interest in mathematics and promote self learning.
  • Best practices of 2019-2020
  1. Arranging talks from corporate sector to give students an overview of job opportunities for mathematicians in that sector. 
  2. Encourage students to widen their perspective and knowledge by reading about a topic in mathematics going beyond the syllabus 
  3. Encourage students to use the department library to study and develop an interest in mathematics and promote self learning. 
  • Industrial Visit
  1.  Industrial Visit to TIFR for a talk on Women Scientists by Leon Jakthajan on 10th January 2017.

Achievements- Students

• Rajashree.S-IV rank ,Second rank for mathematics in 2009.

• Devareddy Sandhya secured I rank in B.Sc course Mathematics for three years and gold medal from Bangalore University in 2010.

• Shreti Garg secured I rank in B.Sc course Mathematics for three years and gold medal from Bangalore University in 2016.

• Sahana K S secured I rank in B.Sc course Mathematics for three years and gold medal from Bangalore University in 2017.

Events conducted by the department

1) Workshop- A two day workshop on scilab and maxima was conducted on 9th and 10th of January 2015.

2) Guest lecture- A guest lecture was organized on 1 September 2016 which was on " Local and global analysis of differential equations" given by Achala. L. Nargund (Head of research centre at M.E.S, Bangalore).

3) Arranged a guest lecture on data analytics for II year students on 6th September 2019.

4) Prepared crossword- quiz prelims for Samagatha fest.

5) A Webinar on "Python for Mathematicians" was conducted by the Mathematics department of mLAC on 7th May 2020 for all BSc students. The talk was given by Mr. Nitin Kumar, BOS member and also SAP Senior Technical Consultant.

6) The Department of Mathematics conducted a webinar on “Differential Equations and Real World Problems” on May 9th 2020 for all BSc students. The talk was given by Prof. Achala L. Nargund, Head and coordinator of P.G. department and Research Centre in Applied Mathematics, M.E.S. College.

7) The Department of Mathematics conducted a webinar on “Applications Of Graph Theory” on May 15th 2020 for all BSc students. The talk was given by Dr. K.N Meera, Assistant Professor Mathematics, Amrita School of Engineering.

8) The faculty of Department of Mathematics, participated in the Online Workshop titled “MCQ import process for Online Examination”, on the 3rd July 2020, conducted by Examination centre, mLAC.

 

Syllabus

Title Year Download
BSc.PCM (2016-2019) 01 Jun, 2016 Download
BSc.PMCs (2016-2019) 01 Jun, 2016 Download
Bsc PMCs (2019-2021) 03 Jul, 2019 Download
Bsc PCM (2019-2021) 03 Jul, 2019 Download

Course Outcome

 

Course Outcomes – Mathematics

1st Year

I Sem MAT.T1-1 [CO1.1 Row reduced echelon form, normal form is introduced to help in solving the system of equations using matrix method supplemented with free mathematical software. The mathematical software helps students in completing the projects/real world problem with ease.]

I Sem MAT.T1-1 [CO1.2 The continuation of the chapter Differential calculus I from II PUC level, helps them to learn the differentiation at higher orders and the partial derivatives which help them to learn the basics concepts of higher mathematics.]

I Sem MAT.T1-1 [CO1.3 The continuation of calculus to continuity, discontinuity, related topics through the mean value theorems their proofs, examples and verifying the same through the mathematical software like maxima and Scilab as a practical component. The introduction of Taylor's series and Maclurin's series completes the chapter.]

I Sem MAT.T1-1 [C01.4 Introduction to Number theory gives us an experience of fun with numbers, their importance and rich heritage apart from a thorough understanding of the basic tools of pure mathematics that is groups introduced in the II Semester.]

I Sem MAT.P1-1 [Introducing the free open source soft-wares namely SCILAB and MAXIMA.]

I Sem MAT.P1-1 [To execute program using scilab for verifying the solutions worked out manually for the  problems involving matrices under the chapter algebra.]

I Sem MAT.P1-1 [The above helps students to use the software while solving real world problems.]

I Sem MAT.P1-1 [To execute program using maxima for verifying the solutions worked out manually for the  problems under the chapter differential calculus.]

II Sem MAT.T2-2 [CO2.1 Introduction to the polar co-ordinates, helping them to look at the polar tangents, related things, helpful in tracing the curves. Visualizing the curves, and exploring the nature area, volume etc through the mathematical software is a matter of hands-on session to the students creating a research culture, which is a necessary in today's world.]

II Sem MAT.T2-2 [CO2.2 The continuation of Integral calculus from II PUC level helps them to apply the awesome reduction formulae and enjoy the rate at which the example gets reduced so instantly. Visualizing the curves, and exploring the nature area, volume, etc. through the mathematical software is a matter of hands-on session to the students creating a research culture, which is a necessary in today's world.]

II Sem MAT.T2-2 [CO2.3 Sequence of real numbers is an important concept in pure mathematics wherein they come across various types of sequences, their nature in different contexts, various theorems to help in discussing their nature. Later, this helps the students in learning the chapter series, of equal importance in pure mathematics.]

II Sem MAT.T2-2 [CO2.4 The continuation of Differential equations from II PUC, intentionally introduced to like, learn, enjoy solving the types of first order differential equations, understand them by plotting graphs in mathematical software, termed as FOSS tools. The above chapter helps them in projects in mathematical biology and interpreting the real-world problem in interdisciplinary areas.]

II Sem MAT.P2-2 [Executing program using scilab to visualize the various cartesian and polar curves and their properties.]

II Sem MAT.P2-2 [Executing program using maxima for verifying the solutions worked out manually for the problems under the chapter sequences, differential calculus and differential equations.]

2nd Year

III Sem MAT.T3-3 [CO3.1 Group theory involves basic concepts of abstract mathematics and related concepts, a must for students inclined towards pure mathematics.]

III Sem MAT.T3-3 [CO3.2 After the ode of first order in the previous semester , the third semester syllabus has higher order differential equations specially of order 2 and 3 to find the solutions in various types and explore the vastness of differential equations. To conclude, the simultaneous differential equations and their solutions, followed by total and simultaneous differential equations and their solutions.]

III Sem MAT.T3-3 [CO3.3 Series of real numbers involve finding of the nature of series by various methods through several theorems and most fascinating summation of different series.]

III Sem MAT.T3-3 [CO3.4 Introduction to basics of statistics. The interpretation of statistical data is studied through the concepts of correlation and regression. The above is also available as a lab component under the FOSS tool R-programming.]

III Sem MAT.P3-3 [Introducing the free open source software R and R studio.]

III Sem MAT.P3-3 [Executing program using scilab for verifying the solutions worked out manually for the problems under the chapter group theory.]

III Sem MAT.P3-3 [Executing program to verify the solutions worked out manually for the problems under the chapter series and differential calculus using maxima.]

III Sem MAT.P3-3 [Executing R programming for verifying the solutions worked out manually for the problems under Statistics]

IV Sem MAT.T4-4 [CO4.1 Group theory incorporates, the further topics like order of an elements involved in understanding cyclic groups, theorems, variety of examples to understand the above said abstract concepts.]

IV Sem MAT.T4-4 [CO4.2 Analysing the curves, limits of integration through the sketches of the different curves to solve double and triple integration. They have their applications in finding the area, surface area and volume. The visualization of the above in mathematical software is commendable.]

IV Sem MAT.T4-4 [CO4.3 Integral theorems help in connecting line integrals, surface integrals and volume integrals. Has wide applications in engineering mathematics.]

IV Sem MAT.T4-4 [CO4.4 Discrete and Continuation distributions are introduced to solve some simple problems. Students develop critical computing knowledge with statistics which helps them in taking up projects an internship in data analysis. The above is also available as a lab component under the FOSS tool R-programming.]

IV Sem MAT.P4-4 [Executing program using scilab for problems under the chapter group theory.]

IV Sem MAT.P4-4 [Executing program using maxima for verifying the solutions worked out manually for the problems under the chapter multiple integrals and integral theorem.]

IV Sem MAT.P4-4 [Executing R programming for verifying the solutions worked out manually for the problems under Statistics.]

3rd Year

V Sem MAT.T5-5 [CO5.1 The definition of the algebraic structure ring, examples, theorems and concepts related to the same are studied. The above are vital concepts in abstract algebra have wide applications in various fields of science. The lab component in the above is an appreciable approach.]

V Sem MAT.T5-5 [CO5.2 Introduction to different types of PDE, general form (Clairaut's equation). Solutions of Heat and wave equation and verifying the same with softwares is part of the lab component.]

V Sem MAT.T5-5 [CO5.3 Improper integral throws light on beta and gamma functions which are very special, simple, easy to learn and apply while integrating a certain set of integrals. These integrals are also involved in Laplace transforms, which is a part of their syllabus for next sem. Also helps students to score better amidst the topic in pure mathematics.]

V Sem MAT.P5-5 [Executing program using maxima for verifying the solutions worked out manually for the problems under the chapter rings & fields and partial differential equations.]

V Sem MAT.T6-5 [CO6.1 Differential calculus for scalar and vector fields help in understanding the mathematical physics and hence an interdisciplinary approach trend is set for the students.]

V Sem MAT.T6-5 [CO6.2 Fourier series and transforms help us in understanding that the given function can be expressed as a sum of sine and cosine functions or one of them in a given interval. The plotting of the same and visualizing the graph in different angles is a practical component. Its applications are left to the students for topics of project. The Fourier transform are also a part of the conclusion of the chapter.]

V Sem MAT.T6-5 [CO6.3 Mathematical modelling is introduced to highlight interdisciplinary approach to solve real world problem and interpret the same using mathematical software and promote research culture in students.]

V Sem MAT.P6-5 [Demonstration of differential calculus of scalar & vector fields and Fourier series and transformations using free software maxima.]

VI Sem MAT.T7-6 [CO7.1 The topic linear algebra has concepts of vector spaces, properties, examples, theorems, transformation, different types, examples, changing the transformation into matrices and vice versa. The same can be visualized using the software maple (trial version). The above has applications in image processing.]

VI Sem MAT.T7-6 [CO7.2 Numerical methods involves forward differences, finite differences, interpolation, numerical differentiation, and integration. For certain examples where integration is not possible, numerical integrations are made use of in obtaining approximation solutions.]

VI Sem MAT.T7-6 [CO7.3 The numerical solutions of algebraic, transcendental and non - linear PDE by various methods and program for the same helps the students to do projects and motivates the young mind to the research culture and higher studies.]

VI Sem MAT.P7-6 [Solving algebraic and transcendental equations through the mathematical software scilab.]

VI Sem MAT.P7-6 [Executing program using maxima for verifying the solutions worked out manually for the problems under the chapter linear algebra.]

VI Sem MAT.T8-6 [CO8.1 The harmonic function and the transformation, help in solving a lot of problems in engineering mathematics and projects. The above also form a part of the lab component.]

VI Sem MAT.T8-6 [CO8.2 Mathematical methods involve the definition, properties, problems, and related concepts. Its application in solving differential equations of first order and second order involving is a part of the lab component.]

VI Sem MAT.P8-6 [Executing program using maxima for verifying the solutions worked out manually for the problems under complex analysis and mathematical modelling.]

 

 

Our Faculty

Dr. Nanda Kulkarni

Head of Department

Lakshmi B N

Assistant Professor

Ranjitha D J

Assistant Professor

Shylaja G

Assistant Professor

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