Lecture site:  APM B402A 
Lecture times:  Tuesday, Thursday. 3:30pm4:50pm. 
Discussion sessions 
E01 970537: Friday 5:00p5:50p, AP&M B412 with Alexander Mathers
E02 970538: Friday 6:00p6:50p, AP&M B412 with Nandagopal Ramachandran 
Final Exam time and place 
June 10th, 2019, 3:00pm  6:00pm. Place TBA 
Instructor 
Martin Licht
Email: mlicht AT ucsd DOT edu Office: AP&M 5880E Hours: Wednesday. 2:00  4:00pm. May be subject to change during the quarter. 
Teaching Assistant 
Alexander Mathers
Email: amathers AT ucsd DOT edu Office Hours: Mondays 45pm, Thursday 11:30am12:30pm, AP&M 5412 
Teaching Assistant 
Nandagopal Ramachandran
Email: naramach AT ucsd DOT edu Office Hours: Wednesdays and Thursdays 56pm, AP&M 6436 
Sections  970537, 970538 
Credit Hours:  4 units 
Course content  This course uses a variety of topics in mathematics to introduce the students to rigorous mathematical proof, emphasizing quantifiers, induction, negation, proof by contradiction, naive set theory, equivalence relations and epsilondelta proofs. Required of all departmental majors. 
Formal prerequesite  Math 18 or Math 20F or Math 31AH, and Math 20C. Students who have not completed listed prerequisites may enroll with consent of instructor. 
Homework information  Homework will announced on Fridays. Homework must be submitted to the mailboxes on Friday's before noon. No homework will be accepted in class. All submissions must be in handedin in handwritten form. 
Homework Philosophy  The homework is the most important part of the course. Along with more straightforward problems designed to solidify the basic definitions and concepts, the homework will contain some problems which you might find difficult and are meant to challenge you. Don't worry if you get stuck; the process of thinking hard about a problem and trying different ideas is extremely valuable in itself and important in developing mathematical maturity. Of course, working through the homework is also vital for exam preparation. 
Collaboration Policy  You are welcome to discuss lecture material and homework problems with other students at the stage when you are still formulating ideas. This may be especially useful if, for example, you are confused about definitions or what the problem is asking. The writeup you hand in should be your work alone in your own words, however, and should be written while you are by yourself. While it is also fine to seek hints from classmates that have figured out problems on which you are stuck, you will learn the most if you think about these problems hard on your own first and don't give up too quickly. 
Academic Integrity  Every student is expected to conduct themselves with academic integrity. Violations of academic integrity will be treated seriously. See http://wwwsenate.ucsd.edu/manual/Appendices/app2.htm for UCSD Policy on Integrity of Scholarship. 
Resources recommended in addition 

A+  A  A  B+  B  B  C+  C  C 
100  96.66  96.65  93.33  93.32  90.00  89.99  86.66  86.65  83.33  83.32  80.00  79.99  76.66  76.65  73.33  73.32  70 
Lecture  Content 

# 1, 1T 02.04.2019. 
Administrativa. Examples and Motivation.
Formal logic: Statements, Implications, Equivalences. Truth Values. 
# 2, 1Th 04.04.2019. 
Formal logic:
Propositions and Logical operators: and, or, negation, eitheror.
Truth tables. Further logical connectives.
Composition of logical operations.

# 3, 2T 09.04.2019. 
Set theory: Naive Set Theory. Settheoretical operations. Definition of Sets. Set comprehension. Power sets. 
# 4, 2Th 11.04.2019. 
Set theory:
Union, intersection, difference.
Relations to logical operations and connectives.
Quantifiers: Existence and Universal Quantifiers. 
# 5, 3T 16.04.2019. 
Set theory: Infinite Unions and Intersections. Cardinality. Proofs involving set theory. 
# 6, 3Th 18.04.2019. 
Proofs in combinatorics: Some examples for proofs in combinatorics. Direct proofs. Proofs by induction. 
#7, 4T 23.04.2019. 
Proofs in combinatorics: Proof by induction in combinatorics. 
#8, 4Th 25.04.2019. 
First Midterm
Set theory: Classes. 
26.04.2019: Deadline to change grading option, change units, and drop classes without "W" grade on transcript.  
#9, 5T 30.04.2019. 
Elementary number theory: wellordering principle and divisibility. divisionremainder theorem, prime numbers, greatest common divisor. 
#10, 5Th 02.05.2019. 
Elementary number theory:
Euclidean algorithm, Bezout's lemma. Infinitiy of the number of prime numbers.
Fundamental theorem of arithmetics. Applications.

#11, 6T 07.05.2019. 
Elementary number theory:
Mersenne prime numbers.
Mersenne prime numbers. Two examples for mathematical induction.

#12, 6Th 09.05.2019. 
Second Midterm. 
10.05.2019: Deadline to drop with "W" grade on transcript.  
#13, 7T 14.05.2019. 
Further Set Theory: Ordered Pairs and Cartesian Products. Functions. Graphs. Injectivity, Surjectivity, Bijectivity. 
#14, 7Th 16.05.2019. 
Further Set Theory:
Tuples and Sequences. Relations.

#15, 8T 21.05.2019. 
Further Set Theory: Equivalence Relations. Orders. 
#16, 8Th 23.05.2019. 
Further Set Theory:
Total Orders. Lexicographical ordering on Cartesian Products.
Operations on Equivalence Classes. Modulo Arithmetics.

#17, 9T 28.05.2019. 
Further Set Theory: Modulo Arithmetics continued. 
#18, 9Th 30.05.2019. 
Review and Examples

#19,10T 04.06.2019. 
Review and Examples 
#20,10Th 06.06.2019. 
Review and Examples 
FI 10.06.2019. 
Final Exam. TIME TBA 3:00pm  6:00pm. PLACE TBA (Lecture Room!) 