I have a friend who is interested in learning math. I suggested that he learns mathematical logic. He has never learnt mathematical logic before, however I believe he has all the necessary prerequisites for a first course in mathematical logic.
I'd like to find good online lectures for a first course in mathematical logic. The lectures should form a complete course. It would be great if someone can help me.
Thanks a lot.
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This is a very popular & free Stanford course from Coursera (a MOOC site). Suggested background is only high school mathematics and it consists of not only lectures, but assignments and practice to reinforce the skills you gain.
The goal of the course is to help you develop a valuable mental ability – a powerful way of thinking that our ancestors have developed over three thousand years.
Mathematical thinking is not the same as doing mathematics – at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself. The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box – a valuable ability in today’s world. This course helps to develop that crucial way of thinking.
The course is offered in two versions. The eight-week-long Basic Course is designed for people who want to develop or improve mathematics-based, analytic thinking for professional or general life purposes. The ten-week-long Extended Course is aimed primarily at first-year students at college or university who are thinking of majoring in mathematics or a mathematically-dependent subject, or high school seniors who have such a college career in mind. The final two weeks are more intensive and require more mathematical background than the Basic Course. There is no need to make a formal election between the two. Simply skip or drop out of the final two weeks if you decide you want to complete only the Basic Course.
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There is "introduction to logic" (https://www.coursera.org/course/intrologic) on Coursera. I have taken this course. It was one of the best courses I have participated in on Coursera.
From the course page:
What should I know to take this class?
The course has no prerequisites beyond high school mathematics. You should be comfortable with symbolic manipulation techniques, as used, for example, in solving simple algebra problems. And you need to understand sets, functions, and relations. However, that's all. If you have this background, you should be fine.
I do think that most mathematical logic courses presuppose some "mathematical maturity" (or at least the background knowledge you get from a good introductory logic course). So I rather doubt that math logic, properly so called, would be a good way in to "learning math".
If however you do want some suggestions of introductory logic books, some freely available online, look at early sections of the annotated Guide which can be obtained from http://www.logicmatters.net/tyl/ [And for beginners working by themselves, books will always trump online notes, let alone video courses, as they can be more expansive and detailed in a way beginners need. For example, Stephen Simpson online notes on mathematical logic are predictably excellent, but they are surely too terse as for stand-alone learning -- though they no doubt serve hist student brilliantly to back up his lectures, and will serve others very well as snappy revision material. See http://www.personal.psu.edu/t20/notes/logic.pdf ]
I leave it others to suggest other routes into mathematics.