this paper extends the scope of algebraic computation based on a non standard × to the more basic case of a non standard +, where standard means associative and commutative. two physically meaningful examples of a non standard + are provided by the observation of motion in special relativity, from either outside (3d) or inside (2d or more), we revisit the “gyro”-theory of ungar to present the m...

The impact of computers on teaching of mathematics is reviewed, to demonstrate a need to reorganise curriculum in mathematics to meet the needs of students of science and engineering in an era of abundant computers and sophisticated software for symbolic computation. Examples are presented of graphical enhancement of teaching of various mathematical concepts.

We are now investigating an "executable" fragment of classical mathematics for testing formal proofs to make formal proof developments less laborious. Several theories of execution of full classical proofs are known. In these theories, some kind of abstract values such as continuations, are necessary. It makes them illegible from computational point of view, although they are mathematically int...

In this lecture I will talk about three mathematical puzzles involving mathematics and computation that have preoccupied me over the years. The first puzzle is to understand the amazing success of the simplex algorithm for linear programming. The second puzzle is about errors made when votes are counted during elections. The third puzzle is: are quantum computers possible?

The present paper is concerned with the existence, meaning and use of the phases of the (complex) Fourier coefficients of pc-sets, viewed as maps from ZZc to C. It explores a particular cross-section of the most general torus of phases, representing pc-sets by the phases of the third and fifth coefficients. On this 2D torus, triads take on the wellknown configuration of the Tonnetz. Some other ...

1 Department of Mathematics and Center for Computation & Technology, Louisiana State 5 University, Baton Rouge, LA 70803, USA. [email protected] 6 2 Department of Mathematics and Center for Computation & Technology, Louisiana State 7 University, Baton Rouge, LA 70803, USA. [email protected] 8 3 Department of Mathematics and Center for Computation & Technology, Louisiana State 9 University, B...

‎This paper extends the scope of algebraic computation based on a non standard $times$ to ‎the more basic case of a non standard $+$‎, ‎where standard means associative ‎and commutative‎. ‎Two physically meaningful examples of a non standard $+$ are ‎provided by the observation of motion in Special Relativity‎, ‎from either ‎outside (3D) or inside (2D or more)‎, ‎We revisit the ``gyro''-theory ...