What we're about
This is a math lecture series in two parts. The first part is intended to bring someone with an understanding of simple numerical algebra to a basic understanding of conventional computational mathematics in five lectures, usually two every two weeks. The second part is intended to bring someone who has a basic understanding of computational mathematics to an understanding of a new proof with important consequences for encryption, hardware design, software design, process design, control systems, logistics, the future course of computational mathematics, and the future of computational devices.
So, this lecture series is appropriate for precocious 8th graders as well as people with GEDs interested in becoming programmers, people with degrees in various engineering fields, or people with doctorates in formal logic, computational complexity, or connectionist topology.
Two lectures will be presented during each session. Sessions are held on the first and third Thursdays of each month.
For the first five lectures, the class plans are designed to show that the core of computational mathematics is easy to understand – in fact, some parts have been taught in public school as early as the 4th and 8th grades. Additionally, the class plans emphasize notational interpretation and how the presented subjects may be practically used and how the subject matter relates to other branches of mathematics. It is hoped that this emphasis will enable students to read beyond their classroom coursework and encourage them to do so.
The first five lectures cover accelerated introductions to the following subjects:
1. Naïve finite set theory, relations, mappings, and basic formal logic. The foundational language of mathematics.
2. Linear algebra. Useful to every branch of science and engineering.
3. Graph theory. Introduces important vocabulary that describes structures that organize data and objects.
4. Practical computational performance.
5. Theory of computational complexity. Describes how complexity is measured, classes of complexity, and an important problem: the Satisfaction problem.
For people who already have an education in many of these subjects, the first five lectures can be productively attended on a piecemeal basis. Some of these lectures include adjustments to the conventional terminology which are intended to correct some conceptual weaknesses that tend to create confusion further down the road. A summary of the terminological adjustments will be made available prior to the beginning of the second part.
Prerequisite for the first five lectures is a practical understanding of: addition, subtraction, multiplication, division, exponents, logarithms, the use of variables, what a polynomial is. In addition, these lectures will be easier to understand if attendees have some experience with computer programming.
The lectures after the first five in the series cover the following subjects:
1. The DPLL and CDCL algorithms and introduction to advanced logics. Logic that makes more sense.
2. CNF topological observations. Advanced vocabulary for describing logical structure & structural diagramming.
3. Counter-assertion. The mechanics of moving contradictions.
4. The Rain of Strepsiades. Choosing a direction for moving a contradiction.
5. Rain is productively different. An example that is hyper-polynomial for other methods and polynomial for Rain.
6. Impetus Flow diagramming. A notation for illustrating counter-assertions and the conditions they create and operate within.
7. Single-contradiction motion. A catalog of the ways that a single contradiction can move and how that motion changes depending on circumstances.
8. Multi-contradiction interference. A catalog of the ways that the motion of one contradiction may complicate the circumstances under which other contradictions move.
9. Reversals. A catalog of the ways that the motion of contradictions may re-traverse a contributing path segment in the opposite direction and what may cause such motion.
10. Worst-case scenario for Rain. Examining structural options and eliminating options that are less efficient at providing high-cost traversals of an expression.
11. Computing the actual worst-case cost of dynamic farthest-reversal Rain. An exposition of the cost arithmetic for the presented version of the Rain of Strepsiades.
12. Discussion of other versions of Rain.
13. Opportunities and hazards. A discussion of likely mathematical, technical, market, and social consequences of the existence of the Rain of Strepsiades.
The lectures in the second part of the series should be attended in order because they will present new notations that are used in subsequent lectures, unusual conceptual distinctions, or intermediate conclusions that are necessary for validating the rest of the argument.
Prerequisite for the second part of the lecture series is an understanding of the subjects in the first part.
It is expected that this lecture series will be repeated in order to give people who missed or did not quite understand an important lecture to catch up and, of course, to expose a new cohort to the subject matter.