MATH 200: Introduction to Mathematical Reasoning
James Cook's Mathematical Reasoning Homepage

Resources for Math 200 of Spring 2025:
  1. Course Planner: this has the day-by-day plan for the course. Like a syllabus, but without the annoying policy bloat.

  2. Lecture Notes: wrote these for Math 200 of Spring 2025, essentially this is the text for this course.

  3. Introduction to Mathematical Reasoning (Math 200-001) of Spring 2025 Playlist on You Tube:

  4. Required Homework (Missions) for Math 200:

  5. There will be quizzes, just about every week, these are very quick and usually just test your ability to cite definitions correctly.

  6. Proof that e is irrational (this proof is due to Fourier, I found it on Wikipedia) Fourier's Proof that e is not a rational number
Resources from past teaching:
Most of the materials below are from when I taught Math 200 in Spring 2009.

Syllabus from 2009 (we had freedom to actually write these back then, can you imagine!)

Lecture Notes from previous courses:

  • Course Notes (from 2009, I used these in part to create the new 2025 notes)

    • Technically, these are not the course notes for Math 200, but Math 115 has much overlap with the first few weeks of our course. Naturally, Math 115 is an easier course, however you may learn something from Ginny's notes. Peruse these for added perspective if you wish. Beware the truth table notation in Math 115 is sort-of weird. Also I don't endorse their definition of "implication". Anyhow,
    1. Logic without math
    2. Truth tables
    3. Biconditionals
    4. Basics of sets
    5. Venn Diagram Problems ( some of these are a bit much for Math 200, ha ha poor Math 115 students hee hee hee...)
    6. Unions, Intersections, Cartesian Products

    Homework Recommendation from past course:
    Homework in advanced mathematics is just as important as it was in calculus, algebra and trigonometry. However, in practice most advanced math courses are not about building skill in calculations. Rather, the focus is on absorbing new definitions and concepts. Homework in advanced mathematics courses is more often about gaining conceptual skill. As we work more and more "proofs" we gain an understanding of what the purpose of doing proofs is. Mathematical maturity is not gained overnight, but rather in a series of small but consequential battles. You need to be determined to persevere against the homework even when it seems to be pointless. There is a point, you'll see it in time.

    These are from A Transition to Advanced Mathematics, 4th Edition (probably, I took this course from that textbook circa 2000 and taught it with this book around 2009) by Smith, Eggen and St. Andre.
    1. Logic and Proofs
    2. Set Theory and Induction
    3. Relations
    4. Functions
    5. Cardnality
    6. Algebraic structures
    General Advice: When confronting many "proof" problems in this course (and in more advanced abstract math courses) you ought to ask yourself:
    1. What information is given in the proof?
    2. What is not given? What are we trying to show?
    3. What are the definitions that apply?
    It is not usually the case that you will find the same proof in my notes or the text. Definitions are key, I cannot emphasize this enough. I have provided a wealth of solved problems for your convenience. Some of those problems are a little more advanced than your homework, but there is something to learn in most everything I solved.

    Section # Extra Examples Due Date Assignment Description / Hints
    Sec. 1.1 math logic Jan. 16 2[b,h,k], 3h, 4[b,g,j](proof by truth table), 8[a,b], 9a, 10[c,e,i], 11a Propositions and Connectives, Proof by Truth Tables
    Sec. 1.2 math logic Jan. 23 4[b,c], 7, 9c, 10b Conditionals and Biconditionals
    Sec. 1.3 math logic Jan. 23 5[a,c,d,g,h,j], 7[a,b,c], 8a Quantifiers
    Sec. 1.4 math logic Jan. 23 5[a,e], 6[a,d], 7[f,g], 9a Basic Proof Methods I
    Sec. 1.5 math logic Jan. 30 2[a,c], 3[c,d], 6a, 7a Basic Proof Methods II
    Sec. 1.6 math logic Jan. 30 1[a,c], 2a, 5[b,d,f,g], 6[a,b,c], 7[d,e] Proofs Involving Quantifiers
    Sec. 2.1 Set Theory Feb. 6 4[g,h], 5[a,d], 8b, 11, 14 Set Concepts
    Sec. 2.2 Set Theory Feb. 6 1j, 2[f,h], 3[a,e,k], 4[a,b,c], 10[a,d,f], 13[a,b,c,d], 14[b,d], 16[c,e,g] Set Operations, focus on set equality
    Sec. 2.3 Set Theory Feb. 13 1[c,g,k], 6[a,b], 9 Indexed Families of Sets
    Sec. 2.4 Set Theory Feb. 13 8[a,d,e,m,n,u,t] Induction
    Sec. 2.5 Set Theory Feb. 13 2(use PCI), 5b, 6[b,d], 7, 9 Fibonacci numbers, Division Algorithm, WOP.
    Sec. 3.1 Relations Feb. 20 1a, 2, 5[a,b,c], 9[e,g], 12, 15 Relations
    Sec. 3.2 Relations Feb. 20 1[c,f,h], 2[a,c,h], 8, 9, 12a Equivalence Relations
    Sec. 3.3 Relations Feb. 20 2[a,b,c,d], 3a, 4, 7, 8b Partitions
    Test I . Feb. 24 Test I Chapters 1,2 and 3
    Sec. 4.1 Functions Mar. 6 1[b,f,h,i], 3[e,h,i], 4[b,e], 6[b,d], 11, 16c functions as relations
    Sec. 4.2 Functions Mar. 6 1[b,d,f], 3[a,e,g,i], 4, 5, 6, 7c(many correct answers), 12[b,d], 16b, 18 constructions of functions
    Sec. 4.3 Functions Mar. 6 1[a,b,c,h,j], 2[a,b,c,h,j], 4, 5, 8[a,b,c,d,e,f] one-one and onto
    Event . Mar. 9-13 Spring Break The "Holidays"
    Sec. 4.4 Functions Mar. 20 2[a,b,c,e], 8[b,c], 11, 14a, 16, 18 images of sets
    Sec. 5.1 Cardinality Mar. 27 1, 4, 5[d,g], 6b, 14, 17 Equivalent Sets
    Sec. 5.2 Cardinality Mar. 27 1[a,d,h], 2a, 2f, 5[a,b,c,e,g], 9, 11 Infinite Sets
    Sec. 5.3 Cardinality . no homework, however, will likely cover Theorems of this section in class Countable Sets
    Sec. 5.4 Cardinality Mar. 27 7, 8[b,c] Ordering of Cardinal Numbers
    Sec. 6.1 Algebra Apr. 3 4[a,b,d,e,f,g,h,i], 7[a,b], 14[b,d], 15[a,b,c,d,f] Algebraic Structures
    Sec. 6.2 Algebra Apr. 3 3, 6[a,b,d], 7, 8[a,c,d], 9a, 10, 13, 17, 18[a,d] Groups
    Sec. 6.3 Algebra Apr. 10 6, 7[a,b], 9b, 17, 18a Subgroups
    Sec. 6.4 Algebra Apr. 10 3, 7[a,b], 19, 21 Operation Preserving Maps
    Sec. 6.5 Algebra Apr. 10 1[b,c,e], 2, 5, 7[a,c], 14 rings and fields
    Event . Apr. 13 . Easter Break
    . Test 2 Review Apr. 14 select problems Review For Test 2
    Test II . Apr. 16 Test II Chapters 4,5 and 6
    . Proof Day I Apr. 21 Proof Presentations (10 minute) Proof Day I
    . Proof Day II Apr. 23 Proof Presentations (10 minute) Proof Day II
    . Final Review Apr. 28 . Review For Final
    Final . at official date at official time comprehensive




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    Last Modified: 1-29-25