Lecturer

                                School of Engineering 

                                Edith Cowan University

                                Joondalup, Western Australia.

                                Office:  JO 05.206

                                Tel:    +61-8-6304-5082 

                                E-mail:    t.rai@ecu.edu.au

Semester 1, 2008

Courses:

• MAT 3315: Biostatistics: Wed. 11:30-1:30 and Thu. 1:30 - 3:30, JO 08.206

• MAT 2251: Optimisation and Networks: Wed. 4:30 - 8:30, room JO 05.219 (lecture),  JO 05.133 (tutorial)

• MAT 1114: Introductory Statistics: Mon. 12:30-2:30 and Tue. 10:30 - 11:30 (lectures), JO 07.102; tutorials as sssigned. 

• MAT 1114: Introductory Statistics:  Online

Office Hours:

                Mon 12:30 - 2:30
                Tues 10:30 - 12:30 & 1:30 - 3:30
                Wed  1:30 - 3:30                 
                Thu, Fri  9:30 - 11:30

Previous Teaching

• At Edith Cowan University, Joondalup, Western Australia
  

• MAT 3101: Statistical Research Methods
• MAT 1184: Problem-solving and Modelling
• MAT 3315: BioStatistics
• MAT 2251: Optimisation and Networks
• MAT 2214: Applied Statistics
  
• MAT 1114: Introductory Statistics

• At University of Missouri - St. Louis
  

• Math 4550: Combinatorics
  
• Math 4450: Linear Algebra
•  Math 4350: The Theory of Numbers (with cryptology)
• Math 2450: Elementary Linear Algebra

 

• At Centennial College:

  • MATH 185 --- Mathematics for Computer Systems 2

  • MTH 110 --- Logic and Problem Solving Strategies

  • MATH 175 --- Mathematics for Computer Systems 1

  • Integral Calculus

  • Mathematics of Finance

  • Technical Mathematics

  • Elementary Statistics
    

   

• At Seneca College:

  • Applied Calculus

  • Differential Calculus

  • Applied Problem Solving

   

• At Virginia Tech:

  • Multivariate Calculus

  • Vector Geometry

  • Linear Algebra

Research

• Cryptography

  • Securing Noncommutative Polly Cracker-type cryptosystems against chosen-ciphertext attacks, with S. Bulygin (to appear, JSC)

  • Abstract
  • Preprint Version
    

  • A public-key cryptosystem based on noncommutative Gröbner bases , with Ed Green , presented at  Cryptography 2004, Melbourne, 2004

  • Infinite Gröbner Bases and Noncommutative Polly Cracker Cryptosystems, Ph.D. dissertation, Virginia Polytechnic Institute and State University

   

• Commutative Artinian Algebras

  • Gröbner bases for ideals of multivariate polynomial rings over principal ideal rings

  • The relationship between commutative local artinian rings and finite-dimensional algebras over a field

Recent Talks/Seminars

• Securing Noncommutative Polly Cracker-type cryptosystems against chosen-ciphertext attacks,  Workshop on Groebner Bases and Cryptography,  Special Semester on Groebner Bases, RISC and RICAM, Linz, Austria, May 1 - 7, 2006
  

• Gröbner bases and cryptography, weekly seminar, Department of Mathematics and Computer Science, University of Missouri - St. Louis, Winter2005

• Polly Cracker-type cryptosystems (colloquium), Department of Mathematics and Computer Science, University of Missouri - St. Louis, Fall 2004.

• Polly Cracker-type cryptosystems, Centre for Computer Security Research, University of Wollongong, Wollongong, Australia, July 19, 2004.

• A Public-key Cryptosystem Based on Noncommutative Gröbner Bases, Cryptography 2004 (Polynomial Based Cryptography), Melbourne, Australia, July 8, 2004.

• Noncommutative Polly Cracker-type cryptosystems, Mathematics and Information Sciences, University of Western Australia, July 2, 2004.

• Noncommutative Polly Cracker-type cryptosystems, GANITA LAB, University of Toronto at Mississauga, May 25, 2004.

• Noncommutative Polly Cracker cryptosystems, Department of Computer Science, University of Toronto, April 23, 2004.

Other Academic Activities and Interests

• Development of curriculum for an applied (bachelor's) degree program in Software Systems: Design, Development and Management, including the writing and succesful defence of a proposal adhering to government guidelines

• Implementation of applied (bachelor's) degree program in Computer and Communications Networks

• Development of computer-based learning modules, including:

               1.  A mathematica-based random question generator

               2.  Mathematica-based modules to study the rotation of conics and the extrema of functions of two variables

               3.  Mathcad-based learning modules for various topics in Discrete/Finite Mathematics

Education

Ph. D. (Mathematics), Virginia Polytechnic Institute & State University, Blacksburg, VA, U.S.A.

M. S. (Mathematics), Virginia Polytechnic Institute & State University, Blacksburg, VA, U.S.A.

B. Sc. (Mathematics), University of Bombay (now University of Mumbai), Bombay (Mumbai), India.

Links of Mathematical Interest

• MegaMath

• American Mathematics Society

• Canadian Mathematics Society

• Australian Mathematics Society

• Virginia Tech Department of Mathematics

• A list of Mathematics Journals
  

Cryptography Links

• International Association For Cryptologic Research

• University of Waterloo: Centre for Applied Cryptographic Research

• University of Toronto: GANITA LAB

• Purdue University: CERIAS

• Macquarie University: Centre for Advanced Computing - Algorithms and Cryptography

• University of Wollongong: Centre for Computer Security Research

• Queensland University of Technology: Information Security Institute

• A more comprehensive list
  

Other Matters of Interest

        The theme for 2007 was  Mathematics and The Brain

        The theme for 2004 was The Mathematics of Networks

        The theme for 2002 was Mathematics and The Genome

May is South Asian Heritage Month in Ontario, Canada.

Mourning the Tragedy at Virginia Tech, April 16, 2007