About this Course
Learn to assume the way in which mathematicians do – a strong cognitive course of developed over hundreds of years.
Mathematical pondering is just not the identical as doing arithmetic – at the least not as arithmetic is usually introduced in our college system. College math usually focuses on studying procedures to unravel extremely stereotyped issues. Skilled mathematicians assume a sure method to remedy actual issues, issues that may come up from the on a regular basis world, or from science, or from inside arithmetic itself. The important thing to success in class math is to study to assume inside-the-box. In distinction, a key function of mathematical pondering is pondering outside-the-box – a helpful means in immediately’s world. This course helps to develop that essential mind-set.
SKILLS YOU WILL GAIN
- Quantity Concept
- Actual Evaluation
- Mathematical Logic
- Language
Syllabus – What you’ll study from this course
3 hours to finish
Week 1
START with the Welcome lecture. It explains what this course is about. (It comes with a brief Background Studying task, to learn earlier than you begin the course, and a Studying Complement on Set Concept to be used later within the course, each in downloadable PDF format.) This preliminary orientation lecture is essential, since this course might be not like several math course you’ve gotten taken earlier than – even when in locations it’d seem like one! AFTER THAT, Lecture 1 prepares the groundwork for the course; then in Lecture 2 we dive into the primary matter. This may increasingly all seem like straightforward stuff, however tens of hundreds of former college students discovered that they had bother later by skipping by Week 1 too rapidly! Be warned. If doable, type or be a part of a examine group and focus on every part with them. BY THE WAY, the time estimates for watching the video lectures are machine generated, primarily based on the video size. Anticipate to spend so much longer going by the lectures sufficiently nicely to know the fabric. The time estimates for finishing the weekly Drawback Units (Quiz format) are a bit extra dependable, however even they’re only a guideline. You could end up taking so much longer.
4 hours to finish
Week 2
In Week 2 we proceed our dialogue of formalized components of language to be used in arithmetic. By now you need to have familiarized your self with the fundamental construction of the course: 1. Watch the primary lecture and reply the in-lecture quizzes; deal with every of the issues within the related Project sheet; THEN watch the tutorial video for the Project sheet. 2. REPEAT sequence for the second lecture. 3. THEN do the Drawback Set, after which you’ll view the Drawback Set tutorial. REMEMBER, the time estimates for watching the video lectures are machine generated, primarily based on the video size. Anticipate to spend so much longer going by the lectures sufficiently nicely to know the fabric. The time estimates for finishing the weekly Drawback Units (Quiz format) are a bit extra dependable, however even they’re only a guideline. You could end up taking so much longer.
4 hours to finish
Week 3
This week we proceed our evaluation of language to be used in arithmetic. Bear in mind, whereas the components of language we’re focusing have specific significance in arithmetic, our predominant curiosity is within the analytic course of itself: How can we formalize ideas from on a regular basis life? As a result of the subjects develop into tougher, beginning this week now we have only one primary lecture cycle (Lecture -> Project -> Tutorial -> Drawback Set -> Tutorial) every week. In case you have not but discovered a number of individuals to work with, please strive to take action. It’s so straightforward to misconceive this materials.
3 hours to finish
Week 4
This week we full our evaluation of language, placing into place the linguistic equipment that enabled, mathematicians within the nineteenth Century to develop a proper mathematical therapy of infinity, thereby lastly placing Calculus onto a agency footing, 300 years after its invention. (You do not want to know calculus for this course.) It’s all about being exact and unambiguous. (However solely the place it counts. We are attempting to increase our fruitfully-flexible human language and reasoning, not exchange them with a rule-based straightjacket!)
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