Mit opencourseware mathematical logic

History of calculus Modern calculus was developed in 17th-century Europe by Isaac Newton and Gottfried Wilhelm Leibniz independently of each other, first publishing around the same time but elements of it appeared in ancient Greece, then in China and the Middle East, and still later again in medieval Europe and in India. Ancient[ edit ] Archimedes used the method of exhaustion to calculate the area under a parabola. The ancient period introduced some of the ideas that led to integral calculus, but does not seem to have developed these ideas in a rigorous and systematic way. Calculations of volume and areaone goal of integral calculus, can be found in the Egyptian Moscow papyrus 13th dynastyc.

Mit opencourseware mathematical logic

March 3rd, The pace of change is mandating that we produce a faster, smarter, better grade of human being. Current systems are preventing that from happening.

Future education system will be unleashed with the advent of a standardized rapid courseware-builder and a single point global distribution system.

Readings | Simplicity Theory | Mathematics | MIT OpenCourseWare

Introduction ——————————————————————————— Within two years a radical shift will begin to occur in the world of education. While many people are making predictions about the direction that education systems are headed, we have found the best predictors to be hidden in the participative viral systems springing to life in the online world, such as iTunes and Amazon.

These bottom-up approaches are quick to develop, participant-driven systems that are closely aligned to the demands of the marketplace. In this paper we will focus on the key missing elements that will cause the disruptive next generation education systems to emerge.

These missing pieces will likely be created within the next two years Mit opencourseware mathematical logic private funding and will cause a dramatic educational shift in less than five years.

The primary missing pieces are a standard architecture for an organic courseware module and the software necessary to build this courseware. The solution to these missing pieces will be a participative courseware-builder that allows the general public to create courses on any conceivable topic.

We expect many companies will attempt to solve this problem, but the market will quickly gravitate towards the one it likes best. Once the market begins to gravitate towards a favorite courseware-builder, a number of new systems will be developed to grow the courseware library, build integrity, make it universally distributed, archive results, and add functionality.

Lessons from the Ancient World During the time of the ancient Greek civilization, several mathematicians became famous for their work. People like Archimedes, Pythagoras, Euclid, Hipparchus, Posidonius and Ptolemy all brought new elements of thinking to society, furthering the field of math, building on the earlier work of Babylonian and Egyptian mathematicians.

A few generations later the Romans became the dominant society on earth, and the one aspect of Roman society that was remarkably absent was the lack of Roman mathematicians.

Rest assured, the scholarly members of Roman society came from a good gene pool and they were every bit as gifted and talented as the Greeks. But Roman society was being held hostage by its own systems. One of the primary culprits for the lack of Roman mathematicians was their numbering system — Roman numerals and its lack of numeric positioning.

But the feature that made Roman numerals so bad was the fact that each number lacked specific numeric positioning and was in fact an equation, and this extra layer of complexity prevented people from doing higher math.

Roman numerals were a system problem, and a huge one at that. They prevented an entire civilization from furthering the field of math and science. Romans were so immersed in their numbering system that they had no clue that it was preventing them from doing even rudimentary math such as adding a column of numbers or simple multiplication or division, a feat still handled by abacus.

It also prevented them from creating some of the more sophisticated banking and accounting systems and restricted academia from moving forward in areas of science, astronomy, and medicine.

Ratchet forward to today. We live in a society where virtually everything is different from the days of the Roman Empire. But what seems so counterintuitive to most is that we are even more dependent today on our systems than the Romans ever were. Most of these systems we take for granted — systems for weights and measurement, accounting, banking, procurement, traffic management, and food labeling.

With each of these systems we are much like the Romans, immersed in the use of these systems to a point where we seldom step back and question the reasoning and logic behind them.

Our systems govern virtually every aspect of our lives. They determine how we live and where we live, what we eat and where we work, where and when we travel, how much money we will make, the job we do, the friends we have, who we marry, and even how long we will live.

Propositional Logic

But much like fish not understanding what water is, we seldom step back to fully understand the context of our existence. Our systems are what control the flow of commerce, govern our effectiveness as members of society, and create much of the stress we face on a daily basis.

The upside is huge. So what are some examples of restrictive systems that are preventing us from doing great things?

Here are just a few examples: Income Tax System — The income tax system is currently the mother of all boat anchors, slowing commerce and the pace of business to a crawl. Half-Implemented Metric System — We are using a half-implemented metric system where we are purchasing cars with 3.Business plan outline pdf mit essays literature review course syllabus wood business card display naturalistic observation definition daily routine of a college student example of data analysis in quantitative research proposal how to write an extended essay introduction social-media-consulting-business-plan pdf, what is strategic.

We are based in North Wales, and serve Wales and the North West we aim to provide quality solutions for small, medium or large businesses regarding web and media services,including site design and hosting, web publicity video. Thomas Frey's futurist predictions will leave you beyond enlightened.

Learn more about the future of education by clicking here! In this course we will cover central aspects of modern formal logic, beginning with an explanation of what constitutes good reasoning.

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Mit opencourseware mathematical logic

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Lecture Notes | Mathematical Statistics | Mathematics | MIT OpenCourseWare