# Math 109 -- Mathematical Reasoning -- Spring 2019

The final grade will composed 20% homework and either (a) 20% of the first midterm, and 20% of the second midterm, and 40% of the final exam or (b) 20% of the best midterm and 60% of the final exam, depending on what gives the better result.

Your course grade will be determined by your cumulative average at the end of the quarter, based on the following scale:

 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

The above scale is guaranteed: for example, if your cumulative average is at least 73, then your final grade will be at least B. However, your instructor may adjust the above scale to be more generous.

## Course Calendar

Lecture Content
# 1, 1T
02.04.2019.
Formal logic: Statements, Implications, Equivalences. Truth Values.
# 2, 1Th
04.04.2019.
Formal logic: Propositions and Logical operators: and, or, negation, either-or. Truth tables. Further logical connectives. Composition of logical operations.
# 3, 2T
09.04.2019.
Set theory: Naive Set Theory. Set-theoretical 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.
#9, 5T
30.04.2019.
Elementary number theory: well-ordering principle and divisibility. division-remainder 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.
#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!)