All answers must be fully justified in complete sentences, except on problems marked with a dagger (†). An expression of the form 3–6† means that the dagger applies to all of problems 3 through 6; something like 7ab† means that the dagger applies to parts a and b of problem 7. Solutions to dagger problems should still be justified, but complete sentences are not required and it should be possible to fit the justification in a single line.
Some problems have a footnote with further explanation.


Lecture 
Assignment 

Week 1 




0 






1 
August 25 
Syllabus 




2 
August 27 
Mathematical definition 




3 
August 29 
Mathematical statements  


Week 2 




4 
September 3 
Propositional calculus 




5 
September 5 
Lists 




Week 3 




6 
September 8 
Lists 




7 
September 10 
Factorials 




8 
September 12 
Sets and subsets 




Week 4 




9 
September 15 
Sets and subsets 




10 
September 17 
Quantifiers 




11 
September 19 
Operations on sets 








Week 5 




12 
September 22 
Review 



Exam 1 
September 23 
Midterm exam 1 
6–7:15pm (tentative) 





All assignments must be typed from now on!
 


13 
September 24 
Exam discussion 




14 
September 26 
LATEX 


Week 6 



15 
September 29 
Proofs 




16 
October 1 
Proofs 




17 
October 3 
Proof by contradiction 






Week 7 




18 
October 6 
Induction 




 




19 
October 8 
Induction 




20 
October 10 
Induction 






Week 8 


21 
October 13 
Lists and factorial (again) 






22 
October 15 
Induction 






23 
October 17 
Sets 




Week 9 

Counting and relations 


24 
October 20 




25 
October 22 






26 
October 24 




Week 10 

Equivalence relations and functions 


27 
October 27 





28 
October 29 





29 
October 31 





Week 11 


30 
November 3 
Review 

31 
November 5 


Exam 2 


32 
November 7 
Bijections 
Assignment 32 [ tex ] [ writeLaTeX ] 

Week 12 


33 
November 10 
Functions 
Assignment 33 [ tex ] [ writeLaTeX ] 

34 
November 12 
Injections, surjections, bijections 
Assignment 34 [ tex ] [ writeLaTeX ] 

35 
November 14 
Injections, surjections, bijections 
Assignment 35 [ tex ] [ writeLaTeX ] 

Week 13 



36 
November 17 
Infinite sets 
Assignment 36 [ tex ] [ writeLaTeX ] 



37 
November 19 
Composition and equality of functions 
Assignment 37 [ tex ] [ writeLaTeX ] 

38 
November 21 
Cardinality 
Assignment 38 [ tex ] [ writeLaTeX ] 



Fall break! 



Week 14 



39 
December 1 
Counting 
Assignment 39 [ tex ] [ writeLaTeX ] 

40 
December 3 
Counting 
Assignment 40 [ tex ] [ writeLaTeX ] 

41 
December 5 
Counting 
Assignment 41 [ tex ] [ writeLaTeX ] 

Week 15 

42 
December 8 
Binomial coefficients 
Assignment 42 [ tex ] [ writeLaTeX ] 

43 
December 10 
Binomial coefficients 
Assignment 43 [ tex ] [ writeLaTeX ] 

44 
December 12 


Exam 3 
TBA 
Final exam 






^{1}You should write your answer as a mathematical definition. Make sure to emphasize the term being defined with italics or an underline. Your definition may rely on the following concepts, which you do not have to define: natural number, integer, addition, subtraction, multiplication, division, zero, one.
^{2}Be very careful with part (d)!
^{3}Exercise 12b asks you to analyze the sums of consecutive cubes but shows examples of sums of consecutive odd cubes. You should be looking at the numbers 1^{3}, 1^{3} + 2^{3}, 1^{3} + 2^{3} + 3^{3}, 1^{3} + 2^{3} + 3^{3} + 4^{3}, etc.
^{4}Also write a precise statement of the Pythagorean theorem.
^{5}The supplement is hyperlinked. If you cannot access it, download it from the course webpage at http://math.colorado.edu/~jonathan.wise/teaching/math2001fall2014
^{6}In each part, you should find a simple formula for the answer that does not use the ∏ symbol. A formula that is more complicated than necessary will not receive full credit.
^{7}On problem 7, just mark the statements true or false. You do not need to write a proof.
^{8}Hint: It may help to look at Exercise 7.16.