Course Goals & Syllabus:
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
primary audience is 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. If that is you, you will need mathematical
thinking to succeed in your major. Because mathematical thinking is a
valuable life skill, however, anyone over the age of 17 could benefit
from taking the course.
The course starts on Monday September 17 and lasts for seven weeks,
five weeks of lectures (two a week) followed by two weeks of monitored
discussion and group work, including an open book final exam to be
completed in week 6 and graded by a calibrated peer review system in
week 7.
Lecture videos are released at 10:00AM PDT on
Mondays and Fridays. (Week 1 is slightly different: The Monday video
release (listed as Lecture 0) is a short welcome and course description,
the Wednesday and Friday releases are of lectures 1 and 2.)
The
lecture topics are (in addition to the initial Instructor’s welcome on the first day of class):
- Introductory material
- Analysis of language – the logical combinators
- Analysis of language – implication
- Analysis of language – equivalence
- Analysis of language – quantifiers
- Working with quantifiers
- Proofs
- Proofs involving quantifiers
- Elements of number theory
- Beginning real analysis
Course URL:
https://class.coursera.org/maththink-2012-001/lecture/index