Intelligent Computer Mathematics OR Mathematics for Intelligent Computer Mathematics Intelligent Computing? OR Franz Lichtenberger Mathematics for Intelligent Computing? Motivation Historical Remarks A Blend of Math Franz Lichtenberger and CS Implementing OMA-PADS Research Institute for Symbolic Computation (RISC-Linz) Johannes Kepler University A Wake-Up Call Linz, Austria CME-EI, August 17, 2018
Intelligent Computer Mathematics OR Mathematics for Intelligent Computing? Status Quo Franz Lichtenberger Motivation ◮ Several (often highly) intelligent mathematical Historical Remarks software systems are used in K-12 math education. A Blend of Math and CS Implementing ◮ Support classical engineering mathematics, i.e., OMA-PADS A Wake-Up Call ◮ solving equations, ◮ differentiation and integration, ◮ geometry ◮ . . .
Intelligent Computer Mathematics OR Mathematics for Intelligent Computing? Status Quo Franz Lichtenberger Motivation ◮ Several (often highly) intelligent mathematical Historical Remarks software systems are used in K-12 math education. A Blend of Math and CS Implementing ◮ Support classical engineering mathematics, i.e., OMA-PADS A Wake-Up Call ◮ solving equations, ◮ differentiation and integration, ◮ geometry ◮ . . . ◮ (Hopefully) more enlightenment than incantation!
Intelligent Computer Mathematics OR Mathematics for Intelligent Computing? Status Quo Franz Lichtenberger Motivation ◮ Several (often highly) intelligent mathematical Historical Remarks software systems are used in K-12 math education. A Blend of Math and CS Implementing ◮ Support classical engineering mathematics, i.e., OMA-PADS A Wake-Up Call ◮ solving equations, ◮ differentiation and integration, ◮ geometry ◮ . . . ◮ (Hopefully) more enlightenment than incantation! ◮ Everything seems fine, BUT ...
Intelligent Computer Mathematics OR Mathematics for Intelligent Computing? Franz The Times They Are A-Changin’ Lichtenberger (Bob Dylan) Motivation Historical Remarks A Blend of Math and CS ◮ Computer Science, especially programming is Implementing OMA-PADS gaining importance. A Wake-Up Call ◮ See for example former president Obama’s “Computer Science For All” – initiative.
Intelligent Computer Mathematics OR Mathematics for Intelligent Computing? Franz The Times They Are A-Changin’ Lichtenberger (Bob Dylan) Motivation Historical Remarks A Blend of Math and CS ◮ Computer Science, especially programming is Implementing OMA-PADS gaining importance. A Wake-Up Call ◮ See for example former president Obama’s “Computer Science For All” – initiative. ◮ Why should this bother us?
Intelligent Computer Mathematics OR Mathematics for Intelligent Computing? Franz The Times They Are A-Changin’ Lichtenberger (Bob Dylan) Motivation Historical Remarks A Blend of Math and CS ◮ Computer Science, especially programming is Implementing OMA-PADS gaining importance. A Wake-Up Call ◮ See for example former president Obama’s “Computer Science For All” – initiative. ◮ Why should this bother us? ◮ My claim: we are teaching the wrong kind of mathematics!
Intelligent Computer Mathematics OR Mathematics for Intelligent Computing? Franz Intelligent vs. Unintelligent Computing Lichtenberger Motivation Historical Remarks “A program is no more than half a conjecture.” A Blend of Math and CS (Edsger W. Dijkstra) Implementing OMA-PADS A Wake-Up Call
Intelligent Computer Mathematics OR Mathematics for Intelligent Computing? Franz Intelligent vs. Unintelligent Computing Lichtenberger Motivation Historical Remarks “A program is no more than half a conjecture.” A Blend of Math and CS (Edsger W. Dijkstra) Implementing OMA-PADS A Wake-Up Call ◮ So, just to write a program is unintelligent computing .
Intelligent Computer Mathematics OR Mathematics for Intelligent Computing? Franz Intelligent vs. Unintelligent Computing Lichtenberger Motivation Historical Remarks “A program is no more than half a conjecture.” A Blend of Math and CS (Edsger W. Dijkstra) Implementing OMA-PADS A Wake-Up Call ◮ So, just to write a program is unintelligent computing . ◮ For intelligent computing one has to ◮ specify the problem, and then to ◮ prove the full conjecture, i.e.,
Intelligent Computer Mathematics OR Mathematics for Intelligent Computing? Franz Intelligent vs. Unintelligent Computing Lichtenberger Motivation Historical Remarks “A program is no more than half a conjecture.” A Blend of Math and CS (Edsger W. Dijkstra) Implementing OMA-PADS A Wake-Up Call ◮ So, just to write a program is unintelligent computing . ◮ For intelligent computing one has to ◮ specify the problem, and then to ◮ prove the full conjecture, i.e., ◮ prove that the proposed program solves the problem.
Intelligent Computer Mathematics OR Mathematics for Intelligent Computing? Mathematics for Intelligent Computing Franz Lichtenberger Motivation Historical Remarks ◮ Problem Specifications need a language with clear A Blend of Math and CS semantics, i.e., Implementing the language of mathematics . OMA-PADS A Wake-Up Call
Intelligent Computer Mathematics OR Mathematics for Intelligent Computing? Mathematics for Intelligent Computing Franz Lichtenberger Motivation Historical Remarks ◮ Problem Specifications need a language with clear A Blend of Math and CS semantics, i.e., Implementing the language of mathematics . OMA-PADS ◮ Proving the conjecture belongs to A Wake-Up Call the methods of mathematics .
Intelligent Computer Mathematics OR Mathematics for Intelligent Computing? Mathematics for Intelligent Computing Franz Lichtenberger Motivation Historical Remarks ◮ Problem Specifications need a language with clear A Blend of Math and CS semantics, i.e., Implementing the language of mathematics . OMA-PADS ◮ Proving the conjecture belongs to A Wake-Up Call the methods of mathematics . ◮ Classical engineering mathematics does not support intelligent computing!
Intelligent Computer Mathematics OR Mathematics for Intelligent Computing? Historical Remarks Franz Lichtenberger Motivation ◮ Around 1980: “Mindstorms” by Seymour Papert Historical Remarks ◮ Shows how children can learn all necessary A Blend of Math and CS concepts of programming. Implementing ◮ LOGO language and “turtle graphics” regarded as a OMA-PADS contribution to math education. A Wake-Up Call
Intelligent Computer Mathematics OR Mathematics for Intelligent Computing? Historical Remarks Franz Lichtenberger Motivation ◮ Around 1980: “Mindstorms” by Seymour Papert Historical Remarks ◮ Shows how children can learn all necessary A Blend of Math and CS concepts of programming. Implementing ◮ LOGO language and “turtle graphics” regarded as a OMA-PADS contribution to math education. A Wake-Up Call ◮ David Stoutemyer (1979): Teach programming with “Computer Symbolic Math", i.e. computer algebra, in math classes!
Intelligent Computer Mathematics OR Mathematics for Intelligent Computing? Historical Remarks Franz Lichtenberger Motivation ◮ Around 1980: “Mindstorms” by Seymour Papert Historical Remarks ◮ Shows how children can learn all necessary A Blend of Math and CS concepts of programming. Implementing ◮ LOGO language and “turtle graphics” regarded as a OMA-PADS contribution to math education. A Wake-Up Call ◮ David Stoutemyer (1979): Teach programming with “Computer Symbolic Math", i.e. computer algebra, in math classes! ◮ This was long before personal computers were available at schools!
Intelligent Computer Mathematics OR Mathematics for Intelligent Computing? Franz The “fourth R” Lichtenberger Motivation Historical Remarks A Blend of Math and CS ◮ Reading, wRiting, aRithmetik, and progRamming Implementing OMA-PADS ◮ The basic skills that every child has to learn in A Wake-Up Call school.
Intelligent Computer Mathematics OR Mathematics for Intelligent Computing? Franz The “fourth R” Lichtenberger Motivation Historical Remarks A Blend of Math and CS ◮ Reading, wRiting, aRithmetik, and progRamming Implementing OMA-PADS ◮ The basic skills that every child has to learn in A Wake-Up Call school. ◮ Many educators opposed the separation of mathematics education from computer science in general, and programming in particular.
Intelligent Computer Mathematics OR Mathematics for Intelligent Computing? Divergence Franz Lichtenberger Motivation Historical Remarks ◮ For a long time I believed that math and CS A Blend of Math education will eventually converge. and CS ◮ The opposite is the case! Implementing OMA-PADS A Wake-Up Call
Intelligent Computer Mathematics OR Mathematics for Intelligent Computing? Divergence Franz Lichtenberger Motivation Historical Remarks ◮ For a long time I believed that math and CS A Blend of Math education will eventually converge. and CS ◮ The opposite is the case! Implementing OMA-PADS ◮ For me this is a sad state because I believe that A Wake-Up Call ◮ mathematical (axiomatic) thinking and ◮ computational (algorithmic) thinking ◮ are just two sides of the same coin,
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