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Methods of Proof in Mathematics - Giantzebra - 04-20-2020
Hello! I don't know if anyone will be able to help me, but hey - may as well give it a shot! At the very least, maybe someone here can direct me somewhere that may help me.
I need a last upper level math course for my ba. I would like it to be four credits, because that will save me from needing to take an extra class.
Question 1: Does anyone know anywhere that I can get a four credit upper level math class?
Question 2:
There is a website called westcott courses. They give credit through Brandman University and are accepted by TESU. They offer an Abstract Algebra course which is 300 level and for four credits. Listed as pre-requisites are linear algebra and Discrete math/Methods of Proof in Mathematics. I have taken discrete math and am planning on taking linear algebra, so I didn't think I would have a problem. However, I found out that they won't take my discrete math as a pre-req because it is more focused on computers. They suggested I take their Methods of Proof course first. The problem is that I don't want to pay for this course that I don't need. So, my question is - does anyone know of a free methods of proof or discrete math course that will cover the material in the syllabus that I'm pasting below?
Thank you so much!
Content Menu
Course Content Menu:
Chapter 1. Sets
1.1. Describing a Set
1.2. Subsets
1.3. Set Operations
1.4. Indexed Collections of Sets
1.5. Partitions of Sets
1.6. Cartesian Products of Sets
Chapter 2. Logic
2.1. Statements
2.2. The Negation of a Statement
2.3. The Disjunction and Conjunction of Statements
2.4. The Implication
2.5. More on Implications
2.6. The Biconditional
2.7. Tautologies and Contradictions
2.8. Logical Equivalence
2.9. Some Fundamental Properties of Logical Equivalence
2.10. Quantified Statements
2.11. Characterizations of Statements
Chapter 3. Direct Proof and Proof by Contraposition
3.1. Trivial and Vacuous Proofs
3.2. Direct Proofs
3.3. Proof by Contrapositive
3.4. Proof by Cases
3.5. Proof Evaluations
Chapter 4. More on Direct Proof and Proof by Contrapositive
4.1. Proofs Involving Divisibility of Integers
4.2. Proofs Involving Congruence of Integers
4.3. Proofs Involving Real Numbers
4.4. Proofs Involving Sets
4.5. Fundamental Properties of Set Operations
4.6. Proofs Involving Cartesian Products of Sets
Chapter 5. Existence and Proof by Contradiction
5.1. Counterexamples
5.2. Proof by Contradiction
5.3. A Review of Three Proof Techniques
5.4. Existence Proofs
5.5. Disproving Existence Statements
Chapter 6. Mathematical Induction
6.1. The Principle of Mathematical Induction
6.2. A More General Principle of Mathematical Induction
6.3. Proof By Minimum Counterexample
6.4. The Strong Principle of Mathematical Induction
Chapter 8. Equivalence Relations
8.1. Relations
8.2. Properties of Relations
8.3. Equivalence Relations
8.4. Properties of Equivalence Classes
8.5. Congruence Modulo n
8.6. The Integers Modulo n
Chapter 9. Functions
9.1. The Definition of a Function
9.2. The Set of All Functions from A to B
9.3. One-to-one and Onto Functions
9.4. Bijective Functions
9.5. Composition of Functions
9.6. Inverse Functions
9.7. Permutations
Chapter 10. Cardinalities of Sets
10.1. Numerically Equivalent Sets
10.2. Denumerable Sets
10.3. Uncountable Sets
Exam #4
Final Exam for Methods of Proof
RE: Methods of Proof in Mathematics - bluebooger - 04-20-2020
I doubt you'll find a free course that gives you any credit, so I doubt they'd accept a non-credit course for meeting the prerequisite
if you live in new york state the SUNY system (State University of New York -- a group of public universities) has a bunch of upper level math courses that can be done online -- probably too expensive if you're out of state though
$1412 for 4 credits
$353 per credit for online out-of-state residents
https://www.esc.edu/tuition-financial-aid/tuition-rates/
list of courses
https://open.suny.edu/courses/search?l=Upper%20Level%20Undergraduate&s=Mathematics
they even have
MATH 4010-01 - Abstract Algebra I: Group Theory
https://open.suny.edu/courses/empire-state-college-university-college-abstract-algebra-i-group-theory-01-fall-2020
RE: Methods of Proof in Mathematics - Giantzebra - 04-20-2020
(04-20-2020, 07:55 PM)bluebooger Wrote: I doubt you'll find a free course that gives you any credit, so I doubt they'd accept a non-credit course for meeting the prerequisiteI think they might accept a non-credit option. Their logic is that students were failing without the pre-req.
if you live in new york state the SUNY system (State University of New York -- a group of public universities) has a bunch of upper level math courses that can be done online -- probably too expensive if you're out of state though
$1412 for 4 credits
$353 per credit for online out-of-state residents
https://www.esc.edu/tuition-financial-aid/tuition-rates/
list of courses
https://open.suny.edu/courses/search?l=Upper%20Level%20Undergraduate&s=Mathematics
they even have
MATH 4010-01 - Abstract Algebra I: Group Theory
https://open.suny.edu/courses/empire-state-college-university-college-abstract-algebra-i-group-theory-01-fall-2020