Foundations of Mathematics (Winter Semesters, MSc Cognitive Systems)
Note that the Winter 2016 course will be taught by Lena Jaeger.. This page only contains information about the course as I teach it.
Anyone can take this course; there is no need to email me to ask whether you can attend.
This course covers basic undergraduate level mathematics needed for the
MSc Cognitive Systems program, and for advanced statistical data analysis in psycholinguistics.
Textbook:
Gilbert and Jordan, 2nd edition, 2002.
Video lectures:
Students should follow the relevant lectures on MIT Open Courseware by Gilbert Strang and Denis Auroux. Please see
here,
here, and
here. Of course, you should not hesitate to consult other sources. Apart from the course textbook, I recommend
Jordan and Smith, fourth edition, but this is optional.
Lecture notes:
available here.
Homework: Six or seven assignments will be handed out. Students must get at least 60\% overall in the homework assignments to qualify to take the final exam. Detailed solutions will be provided; students are expected to work with these solutions themselves to make sure they understand and correct their errors.
Students who want to get extra practice should not hesitate to do the exercises given at the end of each chapter in the textbook (the book provides solutions too).
Schedule:
We have approximately 14 meetings in this course (this varies a bit from year to year). We don't have regular lectures; rather, students are expected to work on their own to read the textbook and watch relevant video lectures on MIT Opencourseware and elsewhere. In the meetings, I will mostly discuss solutions. But I may occasionally give lectures as needed.
The approximate schedule is as follows:
Lecture 
Topic 
Reading 
HW 
1 
Precalculus I: algebra; perm. and comb.; inequalities 
todo 
HW 0 
2 
Discussion: HW0 sols 
todo 
 
3 
Precalculus II: series 
todo 
HW 1 
4 
Solutions HW 1 
todo 

5 
Differentiation 
todo 
HW 2 
6 
Solutions HW 2 
todo 

7 
Integration 
todo 
HW 3 
8 
Solutions HW 3 
todo 
 
9 
Matrix Algebra I 
todo 
HW 4 
10 
Matrix Algebra II, partial derivatives 
todo 
HW 5 
11 
Solutions HW 4 and 5 
todo 
 
12 
Double integrals, change of variables 
todo 
HW 6 
13 
Solutions HW 6 
todo 
 
14 
Final exam 
 
 
Grading: The final grade is based on a 20minute oral exam and the HW assignment grades.