https://www.coursera.org/course/maththink
About the Course
The goal of the course is to help you develop a valuable mental ability
âEUR" a powerful way of thinking that our ancestors have developed over
three thousand years.
Mathematical thinking is not the same as doing mathematics âEUR" 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 âEUR" a
valuable ability in todayâEUR^(TM)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.
They will need mathematical thinking to succeed in their major. Because
mathematical thinking is a valuable life skill, however, anyone over the
age of 17 could benefit from taking the course.
Next session: 17 September 2012 (7 weeks long)
Workload: 8-10 hrs/week hours/week
Course Syllabus
InstructorâEUR^(TM)s welcome and introduction
1. Introductory material
2. Analysis of language âEUR" the logical combinators
3. Analysis of language âEUR" implication
4. Analysis of language âEUR" equivalence
5. Analysis of language âEUR" quantifiers
6. Working with quantifiers
7. Proofs
8. Proofs involving quantifiers
9. Elements of number theory
10. Beginning real analysis
Recommended Background
High school mathematics.
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