Department of Mathematics, Bengaluru Campus

Department of Mathematics is a support department for all Engineering branches in the campus.
Currently the department offers the following courses for the various branches of B.Tech, M.Tech and M.Sc programmes in Odd Semester.

B.Tech, M.Tech and M.Sc Programmes For Even Semester.

The department also offers Ph.D level courses (FDP’s) for the Ph.D students in the School. The courses offered for Ph.D students are as follows:

Other than the regular theory classes, the department conducts tutorial sessions on a weekly basis to improve the problem solving skills of the students. Three faculty members will be present in every tutorial hour in each class. Also additional academic help is provided to weak students in the evenings after regular working hours.

National And International Journal Publications

• Sarada Jayan, K.V. Nagaraja, An optimal numerical integration method over a lune by using an efficient transformation technique, Advanced Studies in Contemporary Mathematics- Accepted, Indexed in Scopus.
• K.V. Nagaraja, Tattwa Darshi Panda, V. Kesavulu Naidu , Optimal Sub parametric Finite Elements for the Computation of Cutoff Wavenumbers in Waveguides, American Institute of Physics (AIP) Conf. Proc. 1715, 020048 (2016); http://dx.doi.org/10.1063/1.4942730 ,Indexed in Scopus.
• Narahari. N, B. Sooryanarayana,  Geetha K. N, Open Neighborhood Chromatic Number of an Antiprism Graph,Applied Mathematics E-Notes May 2015 (International Journal ), Volume No.15( 2015) Page No. 54-62, Indexed in Scopus. 
• V. KesavuluNaidu , P.G. Siddheshwar, K. V. Nagaraja,  Finite Element Solution of Darcy–Brinkman Equation for Irregular Cross-Section Flow Channel using Curved Triangular Elements, Procedia Engineering(Elsevier), 127 ( 2015 ) 301 – 308 ,Indexed in Scopus.
• Dr. B. Venkatesh, “Gauss Quadrature Rules for Numerical Integration over a Standard Tetrahedral Element by Decomposing into Hexahedral Elements”, International Journal Applied Mathematics And Computation, Volume 271, Nov. 2015, Page No. 1062-1070.
• Sarada Jayan, K.V. Nagaraja, Numerical Integration Over Three-Dimensional Regions Bounded By One or More Circular Edges, Procedia Engineering(Elsevier), 127 (2015) 347-353, Indexed in Scopus.
• Sarada Jayan, K.V. Nagaraja, A general and effective numerical integration method to evaluate triple integrals using generalized Gaussian quadrature,  Procedia Engineering(Elsevier), 127 ( 2015 ) 1041 – 1047, Indexed in Scopus.
• Tattwa Darshi Panda, K.V. Nagaraja, Finite Element Method for Solving  Eigenvalue Problem in Waveguide Modes, Global Journal of Pure and Applied Mathematcs, Vol. 11(3), 1241-1251(June 2015), Indexed in Scopus.
• Sarada Jayan, K.V. Nagaraja, Numerical integration over irregular domains using generalized Gaussian quadrature, Proceedings of the Jangjeon Mathematical Society, Vol. 18 (1), 21-30, 2015 (January), Indexed in Scopus.
• B. Sooryanarayana,  Geetha K. N, On the k-metric dimension of graphs, Journal of Mathematics and computational sciences August 2014 (International Journal), Volume No.4( 2014), No.5,Page No. 861-878
• K.V. Nagaraja, V. Kesavulu Naidu, PG Siddheshwar, “Optimal subparametric finite elements for elliptic partial differential equation using higher order curved triangular elements”, International Journal for Computational  Methods in Engineering Science and Mechanics, Vol. 15(2), 83-100 (2014), Publisher: Taylor & Francis, UK, Indexed in Scopus. 
• Sarada Jayan,  K.V.Nagaraja, Numerical integration over n-dimensional cubes using generalized Gaussian quadrature, Proceedings of Jangjeon Mathematical Society, Vol. 17 (1), 63-69, 2014 (January), Publisher: Jangjeon Mathematica Society, South Korea, Indexed in Scopus.
• Dr. B. Venkatesh, “Numerical Integration Over Polygonal Domains using Convex Quadrangulation and Gauss Legendre Quadrature Rules”, International Journal Of Engineering And Computer Science, Volume2, Issue 8, August, 2013 Page No. 2576-2610.
• Gupta D., M. L. Leema, Improving OCR by Effective Pre-Processing and Segmentation for Devanagari Script: A Quantified Study, Journal of Theoretical and Applied Information Technology Vol. 52 No.2 pg. 142-153, June 2013.Geetha K. N, K. N. Meera, Narahari. N,  B. Sooryanarayana, "Open Neighborhood Coloring of Prisms", Journal of Mathematical and Fundamental Sciences (Scopus Indexed) , Volume No. 45. No. 3,  2013, Page No. 245-262, 2013.Geetha K. N, K. N. Meera, Narahari. N,  B. Sooryanarayana, "Open Neighborhood Coloring of Graphs", International Journal of Contemp. Sciences, Volume No.l 8, No. 14, 2013, Page No. ,  675 - 686,  Nov 2013.
• K. N. Meera, B. Sooryanarayana, Strict Boundary Vertices of a graph, Advances and Applications in Mathematics, Vol 12, No. 1, 61-72, May 2013.
• V. Kesavulu Naidu and K.V. Nagaraja, Advantages of cubic arcs for approximating curved boundaries by subparametric transformations for some higher order triangular elements, Applied Mathematics and Computation, Vol.219,Issue 12, 6893-6910, February 2013 (Elsevier).
• K. N. Meera, B. Sooryanarayana, Radiatic dimension of a graph, Journal of computations and modelling, Vol.2,No.4, 109-131, December 2012.
• K. V. Nagaraja and Sarada Jayan, Generalized Gaussian quadrature rules over regions with parabolic edges, International Journal of Computer Mathematics Vol.89, 1631-1640, August 2012 , (Taylor and Francis).
• Deepa Gupta, Mr. Rahul Kumar Yadav, Ms. Nidhi Sajan, Improving Unsupervised Stemming by Fusing Partial Lemmatization Coupled with Data-Based Heuristic for Hind, International Journal of Computer Applications, Vol. 38, 1-8, January 2012.
• Neetu Srivastava, Effect of curvature on oscillatory free convection from an infinite horizontal cylinder embedded in a porous medium, Journal of Applied Mathematics and Fluid Mechanics, Vol.3, 85-94, June 2011.
• K. N. Meera, B. Sooryanarayana, Optimal Outer Sum Number of Graphs, International Journal of Combinatorial Graph Theory and Applications, Vol.4, 23-35, June 2011.
• H. T. Rathod, A. S. Hariprasad, B. Venkatesh, N.L. Ramesh, On Quartic Splines with applications to quadrature over curved domains, International e-Journal of Numerical Analysis and Related Topics, Vol.6, 126-146, March 2011.
• Sarada Jayan, K. V. Nagaraja, Generalized Gaussian quadrature rules over two-dimensional regions with linear sides, Applied Mathematics and Computation, Vol. 217, 5612-5621, February 2011 (Elsevier).
• H. T. Rathod, B. Venkatesh, Gauss Legendre – Gauss Jacobi Quadrature Rules over a tetrahedral Region, International Journal of Mathematical Analysis, Vol.5, 189-198, January 2011.
• V. Kesavulu Naidu, K. V. Nagaraja, The use of parabolic arc in matching curved boundary by point transformations for septic order triangular element and its applications, Advanced Studies in Contemporary Mathematics, Vol. 20, No. 3, 437-456, July 2010.
• H. T. Rathod, H. Y. Shrivalli, K. V. Nagaraja, V. Kesavulu Naidu, On a new cubic spline interpolation with application to quadrature, International Journal of Mathematical Analysis, Vol. 4 No. 28, 1387-1415, July 2010.
• K. V. Nagaraja, H. T. Rathod, Symmetric Gauss Legendre Quadrature Rules for Numerical Integration over an Arbitrary Linear Tetrahedra in Euclidean Three Dimensional Space, International Journal of Mathematical Analysis , Vol.4, 921-928, May 2010.
• H. T.Rathod, Arunkumar Gali, K.V. Nagaraja, K.T. Shivaram, Some composite numerical integration schemes for an arbitrary linear convex quadrilateral region, International e-Journal of Numerical Analysis and Related Topics”, Vol.4, 19-58, March 2010.
• H. T. Rathod ,A. S. Hariprasad, B. Venkatesh, C. S. Nagabhushana, On Quintic Splines with applications to function and integral function approximations, International e-Journal of “Numerical Analysis and Related Topics, Vol.4, 73-103, March 2010.
• H. T. Rathod ,A. S. Hariprasad, B. Venkatesh, C. S. Nagabhushana, The Use of Quintic Splines for High Accuracy Function and Integral Function Approximations, International e-Journal of Numerical Analysis and Related Topics, Vol.4, 104-128, March 2010.
• K. V. Nagaraja, V. Kesavulu Naidu, H. T. Rathod, The use of parabolic arc in matching curved boundary by point transformations for sextic order triangular element, International Journal of Mathematical Analysis , Vol.4, 357-374, February 2010.
• Meenakshi A. R., Jaya Shree D, On Schur Complement in k-Kernel Symmetric Matrices, , Int. Journal of Math.Analysis, Vol. 4, no. 7, 331 – 339, 2010.
• Meenakshi A. R., Jaya Shree D, Product of Range Symmetric Partitioned Matrices, Advances in Fuzzy Mathematics, 221-227, 2010.
• Meenakshi A. R., Jaya Shree D, On k-Kernel symmetric matrices, International journal of Mathematics and Mathematical sciences , Article ID 926217, 8 pages (2009).
• Deepa Gupta, Will Sentences Have Divergence Upon Translation? : A Corpus-Evidence Based Solution for Example Based Approach, Language in India, Vol.9, 1930-2940, October 2009.
• Meenakshi A. R., Jaya Shree D, On Schur Complement in k-Kernel Symmetric Matrices, , Int. Journal of Math.Analysis, Vol. 4, no. 7, 331 – 339, 2010.
• H. T. Rathod , K. V. Nagaraja, V. Kesavulu Naidu, B. Venkatesh, The use of parabolic arcs in matching curved boundaries by point transformations for some higher order triangular elements, Finite Elements in Analysis and Design, Vol. 44, 920-932, August 2008.
• H. T. Rathod , K. V. Nagaraja, Gauss Legendre Quadrature over a Triangle, Journal for Science, Engineering and Technology,Vol. 17, No.1. pp 1-8 (2005).
• H. T. Rathod , B. Venkatesudu, K. V. Nagaraja, Gauss Legendre Quadrature Formulae over A Tetrahedron, Journal for Science, Engineering and Technology,Vol. 17, No.2. pp 59-72 (2005).
• H. T. Rathod, B. Venkatesudu, K. V. Nagaraja, Gauss Legendre Quadrature Formulas For Tetrahedra,International Journal of Computational Engineering Science and Mechanics, Vol.6, No.3, 197-205 (2005).
• H. T. Rathod, K. V. Nagaraja, B. Venkatesudu, Gauss Legendre Quadrature over Triangle, Journal of the Indian Institute of Science, Vol. 84, No.5, pp 183-188 (2004).
• H. T. Rathod, K. V. Nagaraja, B. Venkatesudu, Gauss Legendre Quadrature over a Triangle, Acharya Nagarjuna International Journal of Mathematics & Information Technology, Vol.1, No.1, pp 33-52 (2004).

Paper Presented In National And International Conferences

• Radhakrishnan G., Deepa Gupta, Abhishek R., Ajith A., Sudarshan T. S. B., Analysis of Multimodal Time Series Data of Robotic Environment, In the proceeding of 12th International Conference on Intelligent Systems Design and Applications (ISDA), pages:734 – 739, November 27-29, 2012 (Cochin University of Science and Technology (CUSAT), India).
• SaradaJayan, Nagaraja, K. V., Generalized Gaussian quadrature rules over two-dimensional regions with a curved exponential edge, International Conference on Mathematical Sciences in honour of A. M.Mathai, St.Thomas College, Pala, January 3^rd to 5^th 2011.
• SaradaJayan, K V Nagaraja, Numerical improvement on the solution of a two-dimensional heat flow problem in an L-shaped body,56^th  Congress of The Indian Society of  Theoretical and Apllied Mechanics(An International Meet), SVNIT , Surat, Decemeber 19-21, 2011.
• SaradaJayan, Nagaraja, K. V., Generalized Gaussian quadrature nodes and weights for integration over a triangle, International Conference on Fluid Dynamics and it’s Applications, B. N. M. Institute of Technology, Bangalore, July 20^th to 22^nd 2011.
• Sarada Jayan, K. V. Nagaraja, Generalized Gaussian Quadrature Rules over triangle, Proceedings of International Conference in Emerging Trends in Mathematics and Computer Applications-ICETMCA-2010, pages: 175-177, December 2010 (Mepco-Schlenk Engineering College, Sivakasi).
• Eknath Venkataramani, Deepa Gupta, English-Hindi Automatic Word Alignment with Scarce Resources, Proceedings of International Conference on Asian Language Processing (IALP) 2010, pages: 253-256, December 2010(Harbin, Heilongjiang,China).
• Rahul Kumar Yadav, Deepa Gupta, Annotation Guidelines for Hindi-English Word Alignment, Proceedings of International Conference on Asian Language Processing (IALP) 2010, pages: 293-296, December 2010(Harbin, Heilongjiang,China).
• K. V. Nagaraja, V. Kesavulu Naidu, B. Venkatesh, H. T. Rathod, Gauss Legendre – Gauss Jacobi quadrature rules over a triangular region, Proceedings of 52^nd Congress of Indian Society of Theoretical and Applied Mechanics, pages: 232-241, December 2007 (IIT Khargapur).

Research Scholars

International Workshop Organized by the Department

• A National Workshop on “Analytical and Numerical solutions of Non-linear Differential Equations” was conducted by the Department on 18th and 19th March 2011 at Amrita School of Engineering, Bengaluru.
  On this occasion, two invited lectures were organized. One by Dr. P. S. Datti, Professor, TIFR and another by Dr. Pradeep G Siddeshwar, Professor, Department of Mathematics, Bangalore University . Prof. P. S. Datti spoke on backlund transformation and point transformation. Dr. P. G. Siddeshwar gave an interesting talk on ‘Computer assisted analytical and Numerical solutions of non-linear Differential Equations’.
  A hands on MATLAB session was also conducted for the participants of the workshop in which they were introduced to the basics of MATLAB. Two worksheets were prepared by faculty members of the Department, which made the participants well acquainted with some of the applications of MATLAB. 
   

Workshops / Seminars / Conferences Organized

• National Workshop on Graph Theory and its Applications

  The Department of Mathematics organized a two-day workshop on Graph Theory and its Applications from August 6 - 7, 2015. About 30 delegates from various engineering colleges of India and around 30 members including faculty members, research scholars and M.Tech. students from Amrita attended the workshop.
  The workshop began with an inaugural function on 6^th August 2015 at 10.30 AM at Krishna Hall, ASE, Bengaluru. The function was graced by Dr. S. G. Rakesh, Associate Dean and Head, Amrita School of Engineering, Bengaluru Campus, who wished the workshop a grand success. The inaugural session was followed by invited lectures. Eminent speakers like Dr. S. A. Choudum from Christ University, Dr. A. Vijaya Kumar from CUSAT, Dr. B. Sooryanarayana from DR.AIT, Dr. J. Paulraj Joseph from MS university and Dr. S. Somasundaram from ASE Coimbatore delivered talks on current research topics in graph theory spread over several sessions of the workshop on both days.
  A introductory session on the usage of Mathematical software, ‘MATHEMATICA’ in solving research problems on graph theory was also presented by Mr. Girish from Wolfram.

Workshops / Seminars / Conferences Attended

• Paper presented in IDAD-2016 organised at Veltech University in the month of February 2016.

• Dr. B. Sooryanarayana and Ms. K.N.Meera presented paper "Open Neighborhood Chromatic number" in the National Conference on Graph Coloring and its application from 27th – 28th July 2013.

• Dr. B. Sooryanarayana and  Ms. K.N.Meera presented paper "2-Metric dimension in Cartesian Products of Graphs"  in the International Conference on Emerging Trends in Fluid Mechanics and graph theory”, Christ University, Bangalore from 16th-18th Aug 2012.

Faculty Development Programs (FDP) Conducted by the Department

• Dr.Deepa Gupta, Assistant Profesoor, Department of Mathematics along with Dr.B.Veeresh Kumar, Department of Mechanical Engineering conducted a faculty development programme on Soft computing, from December 2012 to March 2013.
• FDP by Dr. B. Venkatesh, Associate Professor on Advanced Numerical Analysis from August 2012 to January 2013.
• FDP by Dr. K. V. Nagaraja, Professor on Engineering modeling and PDE from January 2012 to July 2012.
• Dr. Neetu Srivastava, Assistant Professor, Department of Mathematics along with Dr. Sukanya Saha, Department of English conducted a faculty development programme on Research Methodologies, from January 2012 to May 2012.
• FDP by Dr. P. A. Lakshmi Narayana, Assistant Professor on Linear Algebra and its Applications from January 2011 to June 2011.
• FDP by Dr. K. V. Nagaraja, Professor on Advanced Numerical Analysis from July 2010 to January 2011.

Other than the above FDPs,  the department had organized FDPs by external experts, the details of which are as follows:

• FDP by Dr. Pradeep G. Siddheshwar , Professor, Bengaluru University on Partial differential equations from September 2009 to March 2010.
• FDP by Dr. S. Bhargava , Professor Emiritus, Mysore University on Optimization techniques from January 2009 to May 2009.
• FDP by Dr. S. Bhargava , Professor Emiritus, Mysore University on Linear Algebra from January 2007 to May 2007.

Invited Talk/ Guest Lecture

• Dr. K. V. Nagaraja , Attended National Workshop on Parabolic Differential Equations and Applications to Image Processing during 26^th -29^th October 2015, at Sri Sathya Sai Institute of Higher Learning, Puttaparti.
• Dr. K. V. Nagaraja has delivered an invited talk titled on “Introduction to Finite Element Method” on 1^st August 2014 in a “One-Week Faculty Development Programmee” Organized by the Department of Mathematics, Malnad College of Engineering, Hassan during 28^th July – 2^nd August 2014. The workshop was sponsored by TEQIP-II (Technical Education Quality Improvement Programme-II).
• Dr. K. V. Nagaraja has delivered  an invited talk titled on “Finite element solution of Darcy-Brinkman and Darcy-Forchheimer-Brinkman equation for some flow channels using triangular elements” on 27^th June 2014 in a “Two-Week International Workshop on Computational Fluid Dynamics” Organized by the Department of Mathematics, BMS College of Engineering, Bangalore during 23^rd June – 5^th July 2014. The workshop was sponsored by TEQIP-II (Technical Education Quality Improvement Programme-II).
• “Support Vector Machine- kernels and Kernel Trick”, TEQIP-II sponsored Faculty Development Programme on “Knowledge Mining using Machine Leaning and its Applications” during 23^rd January 2014 to 25^th January 2014 at Department of ISE, MSRIT, Bangalore. India.
• “Introduction to Machine Learning & Its Applications”, A Three days workshop on Knowledge Management and Data Analytics for real World Applications (KMDA-13)", during 22^nd July to 24^th July, 2013 at R V College of Engineering, Bangalore, India.
• “Domain Biased Bilingual Parallel Data Extraction and an Unsupervised Hybrid Approach to Align Sentences and Words in Parallel Corpora”, Workshop on " Natural Language Processing and Speech Recognition" on 15^th – 17^th April 2013 at RV College, Bangalore India.
• Dr. K. V. Nagaraja has delivered  an invited talk titled on “Finite Element Method and its Applications”, Two day workshop on “Current Topics in Mathematics”, for Post Graduate Students on 1^st March, 2013 at Christ University.
• “Robotic Data Mining”, 9^th International conference on Emerging trends in physics -2013, on 21^st -22^nd February 2013, Place: St. Joseph's College of Arts and Science(Autonomous), Cuddalore, TN, India.
• “Introduction to Probability Theory and Sampling”, 26^th April, 2012 at PSE School of Engineering, Bangalore, Karnataka, India.
• “Introduction to MATLAB”, 9^th August, 2012 at Jain University Bangalore, Karnataka, India.
• “Introduction to Vector Calculus”, 4^th December, 2012 at PSEIT, South Campus, Bangalore, Karnataka, India.
• “The Role of Natural Language Processing in Electronic Health Domain/Records”, National Seminar on Data Mining and Knowledge Discovery of Medical Data, 28^th – 29^thJuly 2011, organized by Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Bangalore Karnataka, India.