Exams
- Fall 2021 Final
- Fall 2016 Final
- Winter 2015 Final
- Winter 2012 Final
- Fall 2012 Final
- Fall 2016 Midterm
- Winter 2015 Midterm
- Winter 2012 Midterm
- Fall 2012 Midterm
Assignments
- Winter 2012 Assignment 1
- Fall 2012 Assignment 1
- Winter 2012 Assignment 2
- Fall 2012 Assignment 2
- Winter 2012 Assignment 3
- Fall 2012 Assignment 3
- Winter 2012 Assignment 4
- Fall 2012 Assignment 4
- Winter 2012 Assignment 5
- Fall 2012 Assignment 5
- Winter 2012 Assignment 6
- Fall 2012 Assignment 6
- Winter 2012 Assignment 7
- Fall 2012 Assignment 7
Notes
These notes are from my iPad using Neu.Notes+. My handwriting is, at times, atrocious. I blame it on the software.
- Day 1 -Motivation, Notation, and Review
- Day 2 -More Review plus Needed Results on Primes and the Triangle Inequality
- Day 3 -Set Theory Notation and Functions Between Sets; Examples
- Day 4 -Upper and Lower Bounds for Real Numbers, the Completeness Axiom for the Reals
- Day 5 -Nested Interval and Archimedean Properties of the Reals
- Day 6 -Density of the Rationals and Irrationals in the Reals; Injectivity and Surjectivity of Functions
- Day 7 -Cardinality and Results on Countable Sets; Examples
- Day 8 -Countability of the Rationals; Uncountability of the Interval (0,1)
- Day 9 -Cardinality of the Reals; Power Sets
- Day 10 -More on Power Sets; Definition and Examples of Sequences of Real Numbers; Convergence
- Day 11 -Divergence; Partitions; Definition and Examples of Bounded Sequences of Real Numbers
- Day 12 -Monotone Convergence Theorem; Properties of Sequences of Real Numbers; Squeeze Theorem
- Day 13 -Proof of Squeeze Theorem; Definition, Examples, and Properties of Subsequences
- Day 14 -Bolzano-Weierstrass Theorem; Limsup and Liminf; More Sequential Properties
- Day 15 -Yet More Sequential Properties; Metric Spaces: Definition
- Day 16 -Examples of Metric Spaces; Cauchy and Convergent Sequences in a Metric Space; Completeness
- Day 17 -Completeness of the Real Numbers, Equivalent Properties; Series of Real Numbers:Convergence and Geometric
- Day 18 -Equivalence Relations; Examples of Series of Real Numbers
- Day 19 -Cauchy Condensation Test
- Day 20 -Properties of Series of Real Numbers; Comparison Test; Absolute & Conditional Convergence; Alternating Series Test
- Day 21 -Fun with Rearrangements
- Day 22 -The Idea of the Cantor Set; Open Sets in a Metric Space
- Day 23 -Properties of Open Sets; Limit Points in a Metric Space; Closed Sets
- Day 24 -Examples of Open and Closed Subsets of the Real Numbers; Characterization of Closed Sets
- Day 25 -Properties of Closed Sets; Closure and Interior of a Subset of a Metric Space; Compactness: Definition
- Day 26 -Heine-Borel Theorem; Compactness: Equivalences
- Day 27 -Connectedness: Definition, Examples, Equivalences in the Reals
- Day 28 -More on Connected Subsets of the Reals; Topological Examination of the Cantor Set; Hausdorff Dimension
- Day 29 -Functional Limits: Definition, Examples, and Equivalences on the Reals
- Day 30 -Continuity on Metric Spaces; Definition, Examples, Equivalences, Properties
- Day 31 -Topological Mapping Properties of Continuous Functions; Extreme Value Theorem; The Set of Discontinuities
- Day 32 -Derivatives on the Reals: Definition and Examples; Product, Quotient, and Chain Rules
- Day 33 -Intermediate Value Theorem; Local Maxima and Minima, Rolle and Mean Value Theorems; Consequences
- Day 34 -A Continuous, Nowhere-Differentiable Function on the Reals
- Special Day -Constructing the Natural Numbers
- Special Day -The Peano Axioms
- Special Day -Algebraic and Order Properties for Natural Numbers
- Special Day -Constructing the Integers via Equivalence Classes of Pairs of Natural Numbers
- Special Day -Constructing the Rationals via Equivalence Classes of Pairs of Integers
- Special Day -Constructing the Reals via Cauchy Sequences of Rationals
- Special Day -An Explicit Uncountable Family of Transcendental Numbers
