Skip to main content
Side panel
Courses
Programs
Help
Getting Started
Discussion Forums
Help Center & FAQ
Search
Close
Search
Toggle search input
Log in or Sign up
Courses
Programs
Help
Getting Started
Discussion Forums
Help Center & FAQ
MA111: Introduction to Mathematical Reasoning
Sections
Course Introduction
Unit 1: Logic
Unit 2: Sets
Unit 3: Introduction to Number Theory
Unit 4: Rational Numbers
Unit 5: Mathematical Induction
Unit 6: Relations and Functions
Unit 7: Sets, Part II
Unit 8: Combinatorics
Course Feedback Survey
Certificate Final Exam
Resources
Activities
Quizzes
Home
My programs
MA111: Introduction to Mathematical Reasoning
Home
Courses
Course Catalog
Mathematics
MA111: Introduction to Mathematical Reasoning
Recent activity
All participants
MA111: Introduction to Mathematical Reasoning: All participants
Filters
Activities
All activities
All Quizzes
-- Course Introduction --
-- Unit 1: Logic --
-- 1.1: Sudoku and Latin Squares --
-- 1.2: Ken-Ken --
-- 1.3: SET --
-- 1.4: Other Brain Teasers --
-- 1.4.1: Truth Tellers and Liars --
-- 1.4.2: Coin Weighing Puzzles --
-- 1.5: Propositional Logic --
-- 1.5.1: Compound Proposition --
-- 1.5.2: Truth Tables --
-- 1.6: Predicate Logic --
-- 1.6.1: Modus Ponens and Modus Tollens --
-- 1.6.2: Proofs by Contradiction --
-- 1.6.3: Problem Solving Strategies --
-- 1.6.4: Contrapositive and Equivalent Forms --
-- Unit 1 Assessment --
Unit 1 Assessment
-- Unit 2: Sets --
-- 2.1: What Is a Set? Set Builder Notation --
-- 2.1.1: The Empty Set, the Universal Set --
-- 2.1.2: Sets with Sets as Members --
-- 2.2: Building New Sets from Given Sets --
-- 2.2.1: Properties of Union, Intersection, and Complementation --
-- 2.2.2: The (Boolean) Algebra of Subsets of a Set --
-- 2.2.3: Using Characteristic Functions to Prove Properties of Sets --
-- 2.3: The Cartesian Product of Two or More Sets --
-- 2.3.1: The Disjoint Union and Addition --
-- 2.3.2: The Cartesian Product and Multiplication --
-- 2.4.1: The Cardinality of the Power Set of a Set --
-- 2.4.2: The Formula |A| + |B| = |A ⋃ B| + |A ⋂ B| --
-- Unit 2 Assessment --
Unit 2 Assessment
-- Unit 3: Introduction to Number Theory --
-- 3.1: Place Value Notation --
-- 3.2: Prime Numbers --
-- 3.2.1: An Infinitude of Primes --
-- 3.2.2: Conjectures about Primes --
-- 3.2.2.1: The Twin Prime Conjecture --
-- 3.2.2.2: Goldbach's Conjecture --
-- 3.2.2.3: The Riemann Hypothesis --
-- 3.3: Fundamental Theorem of Arithmetic (FTA) --
-- 3.4: Modular Arithmetic, the Algebra of Remainders --
-- 3.4.1: Division by 3, 9, and 11 --
-- 3.4.2: Building the Field Z? --
-- 3.4.3.1: The Addition of Remainders --
-- 3.4.3.2: The Multiplication of Remainders --
-- 3.5.1: The Floor and the Ceiling Functions --
-- 3.5.2: The Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of Two Integers --
-- 3.5.3: The Sigma-Function, Summing Divisors --
-- 3.6: The Euclidean Algorithm --
-- 3.6.1: Another Look at the Division Algorithm --
-- 3.6.2: Solving Ax + By = C over the Integers --
-- Unit 4: Rational Numbers --
-- 4.1: Fractions and Rational Numbers Are Not the Same --
-- 4.2: Representing Rational Numbers as Decimals --
-- 4.3.1: The Square Roots of 2, 3, and 6 are All Irrational Numbers --
-- 4.3.2: Density of Irrational Numbers --
-- 4.3.3: Algebraic versus Transcendental Numbers --
-- 4.4: The Field of Rational Numbers --
-- Unit 5: Mathematical Induction --
-- 5.1: Mathematical Induction Is Equivalent to the Well-Ordering Property of N --
-- 5.2.1: Sums and Products --
-- 5.2.2: Divisibility --
-- 5.2.3: Recursively Defined Functions --
-- Unit 5 Assessment --
Unit 5 Assessment
-- Unit 6: Relations and Functions --
-- 6.1: Binary Relations on a Set A --
-- 6.2.1: Relations that Are Functions --
-- 6.2.2: Injections, Surjections, and Bijections --
-- 6.3: Equivalence Relations --
-- 6.4: Partial Orderings --
-- Unit 6 Assessment --
Unit 6 Assessment, Part 1
Unit 6 Assessment, Part 2
-- Unit 7: Sets, Part II --
-- 7.1: Cantor Diagonalization Theorem: The Existence of Uncountable Sets of Real Numbers --
-- 7.1.1: Proof of the Theorem --
-- 7.1.2: Even the Cantor Set Is Uncountable, the Base-3 Connection with the Cantor Ternary Set --
-- 7.1.3: Other Examples of Uncountable Subsets of R --
-- 7.2: The Rational Numbers Are Countable --
-- 7.2.1: The Proof --
-- 7.2.2: The Algebraic Numbers Are Countable --
-- 7.3: Other Bijections --
-- Unit 7 Assessment --
Unit 7 Assessment, Part 1
Unit 7 Assessment, Part 2
-- Unit 8: Combinatorics --
-- 8.1: Counting Problems as Sampling Problems with Conditions on the Structure of the Sample --
-- 8.2: The Inclusion-Exclusion Principle --
-- 8.2.1: The Case with Just Two Sets --
-- 8.2.2: The Proof --
-- 8.2.3: Other Examples --
-- 8.3: The Pigeon-Hole Principle (PHP) --
-- 8.3.1: The Standard Principle --
-- 8.3.2: Using the PHP Idea in Other Settings --
-- Course Feedback Survey --
-- Certificate Final Exam --
MA111: Certificate Final Exam
Groups
All groups
Sort by
By course order
Date - most recent last
Date - most recent first
Since
Since
Day
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Month
January
February
March
April
May
June
July
August
September
October
November
December
Year
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
Hour
00
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
Minute
00
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
Enable
Unit 1 Assessment
Quiz
Unit 1 Assessment
Unit 2 Assessment
Quiz
Unit 2 Assessment
Unit 5 Assessment
Quiz
Unit 5 Assessment
Unit 6 Assessment
Quiz
Unit 6 Assessment, Part 1
Quiz
Unit 6 Assessment, Part 2
Unit 7 Assessment
Quiz
Unit 7 Assessment, Part 1
Quiz
Unit 7 Assessment, Part 2
Certificate Final Exam
Quiz
MA111: Certificate Final Exam