Videos

Carmen's Core Concepts

These videos are my weekly review videos for Math 135. Note that different classes might have covered topics in a different order but the majority of the content is fairly consistent. These videos highlight what I think were the important concepts for the week.

Again if you didn't cover all the same topics as me this week that is not a sign to be worried. The idea of these videos is to provide you with a brief summary of what happened during the week so that you can get a nice reminder (or a look ahead if you're using these as a look ahead guide for the week!) and hopefully help you on your assignments and while studying for finals. These videos are not meant to replace lectures in any way and are meant as a supplement to lectures.

Each week is separated into videos of similar topics. If you are unsure where exactly the topic you're looking for will be, watch the Table of Contents video, and click on the arrow to be directed to the proper video. Furthermore, once to get to the video you want, you can click the "Table of Contents" button in the bottom right and search for specific words within that video. PS. Sorry about the lighting in the first video.

If you're watching these videos on your mobile device, you will have to download the TechSmith Smart Player app. When you open the videos, click it and you will be directed to the app on the app store. It's free and takes up very little space (only 1.9 MB).

 

Table of Contents TruthTables/ DML/ Logic Direct Proof Methods Divisibility Week 1 pdf Week 1 Alternative Format Week 1 mp4
Table of Contents Divisibility Theorems/Converse/Iff Sets Quantified Statements Negating/Nested Quantifiers Week 2 pdf Week 2 Alternative Format Week 2 mp4
Table of Contents Math To English/Contrapositive Types of Implications/ Contradiction Uniqueness/ Injection/ Surjection/ Division Algorithm Summation and Product Notation Week 3 pdf Week 3 Alternative Format Week 3 mp4
Table of Contents Mathematical Induction Strong Induction/Fibonacci Euclid's Lemma/ FTA Week 4 pdf Week 4 Alternative Format Week 4 mp4
Table of Contents Euclid's Theorem/ GCD(WR)/ Euclidean Algorithm Bezout's Lemma/ GCDCT Mixed GCD Examples/ GCD Tips PAD/ GCDOO/ DBGCD/ CAD Summary of Week 5 Theorems Week 5 pdf Week 5 Alternative Format Week 5 mp4
Table of Contents EEA FTA(UFT)/ DFPF/ GCDPF Tips for GCD Problems LDE/ LDET(1 and 2) Modulus Definition (Most Important definition in the Course) Week 6 pdf Week 6 Alternative Format Week 6 mp4
Table of Contents Part 1 Table of Contents Part 2 Congruence/ CER/ PC CD/ CISR Linear Congruences/ LCT1 Simplifying Congruences Commutative Rings/ Fields/ Congruence Classes/ Well-Defined Addition and Multiplication Tables Week 7 Pt.1 pdf Week 7 Pt.2 pdf Week 7 Part 1 Alternative Format Week 7 Part 2 Alternative Format Week 7 Pt.1 mp4 Week 7 Pt.2 mp4
Table of Contents TFAE/ Inverses/ LCT2 FLT CRT/ SM Cryptography/ Square and Multiply Algorithm Week 8 pdf Week 8 Alternative Format Week 8 mp4
Table of Contents Part 1 Table of Contents Part 2 Exponentiation Ciphers (RSA) RSA Main Theorem RSA Security/ Examples Complex Numbers Intro/ Conjugates Properties of Modulus Polar Coordinates Week 9 Pt.1 pdf Week 9 Pt.2 pdf Week 9 Pt.1 Alternative Format Week 9 Pt.2 Alternative Format Week 9 Pt.1 mp4 Week 9 Pt.2 mp4
Table of Contents PMCN/ DMT Complex Exponential Function/ Complex Roots Polynomial Ring/ Definitions/ DAP Week 10 pdf Week 10 Alternative Format Week 10 mp4
Table of Contents Part 1 Table of Contents Part 2 Polynomial Statements/ RT/ FT Roots Over a Field FTA/ CPN RRT/ CJRT Irreducibile/ Field Matters Long Division/ Multiplicity/ Finding Roots RRT/ CJRT Examples Rationality Week 11 Pt.1 pdf Week 11 Pt.2 pdf Week 11 Part 1 Alternative Format Week 11 Part 2 Alternative Format Week 11 Pt.1 mp4 Week 11 Pt.2 mp4
Table of Contents RQF/ RFRP Examples/ Square Roots of Complex Numbers Week 12 pdf Week 12 Alternative Format Week 12 mp4
Carmen's Core Concepts srt Files

The table below contains all the srt files for the previous CCC videos. If you want to download one, open it, and save the page but change the .txt extension to just .srt.


Table of Contents TruthTables/ DML/ Logic Direct Proof Methods Divisibility
Table of Contents Divisibility Theorems/Converse/Iff Sets Quantified Statements Negating/Nested Quantifiers
Table of Contents Math To English/Contrapositive Types of Implications/ Contradiction Uniqueness/ Injection/ Surjection/ Division Algorithm Summation and Product Notation
Table of Contents Mathematical Induction Strong Induction/Fibonacci Euclid's Lemma/ FTA
Table of Contents Euclid's Theorem/ GCD(WR)/ Euclidean Algorithm Bezout's Lemma/ GCDCT Mixed GCD Examples/ GCD Tips PAD/ GCDOO/ DBGCD/ CAD Summary of Week 5 Theorems
Table of Contents EEA FTA(UFT)/ DFPF/ GCDPF Tips for GCD Problems LDE/ LDET(1 and 2) Modulus Definition (Most Important Definition in the Course)
Table of Contents Part 1 Table of Contents Part 2 Congruence/ CER/ PC CD/ CISR Linear Congruences/ LCT1 Simplifying Congruences Commutative Rings/ Fields/ Congruence Classes/ Well-Defined Addition and Multiplication Tables
Table of Contents TFAE/ Inverses/ LCT2 FLT CRT/ SM Cryptography/ Square and Multiply Algorithm
Table of Contents Part 1 Table of Contents Part 2 Exponentiation Ciphers (RSA) RSA Main Theorem RSA Security/ Examples Complex Numbers Intro/ Conjugates Properties of Modulus Polar Coordinates
Table of Contents PMCN/ DMT Complex Exponential Function/ Complex Roots Polynomial Ring/ Definitions/ DAP
Table of Contents Part 1 Table of Contents Part 2 Polynomial Statements/ RT/ FT Roots Over a Field FTA/ CPN RRT/ CJRT Irreducibile/ Field Matters Long Division/ Multiplicity/ Finding Roots RRT/ CJRT Examples Rationality
Table of Contents RQF/ RFRP Examples/ Square Roots of Complex Numbers
Misconceptions in Math 135

These videos highlight some of the misconceptions in Math 135.

 

Inequalities Inequalities PDF Alternative Format Inequalities mp4 Inequalities srt
Induction Induction PDF Alternative Format Induction mp4 Induction srt
Tutorial Videos

These videos were created beginning in 2015 when I was first hired at the University of Waterloo. I view these more as extra practice problems than I do as a full content review. Feedback and errors can be sent to my email address.

ERRATA: In the Week 10 Polar Coordinates video, I incorrectly simplify $\sqrt{24 - 12\sqrt{3}}$ to $2\sqrt{8 - 3\sqrt{3}}$ when it should be $2\sqrt{6 - 3\sqrt{3}}$. I've corrected this in the pdf but left the video unaltered (it doesn't change much of the content).

 

Tutorial srt Files

The table below contains all the srt files for the previous Tutorial videos. If you want to download one, open it, and save the page but change the .txt extension to just .srt.


Show p and p+1 are prime implies p=2 Negating an Implication and Logical Equivalence
If and Only If Question and Proof A Set Equality Another Set Equality A Calculus Example of Nesting and Negating Quantifiers
An Example of Uniqueness Example of an Injective and Surjective Function
An Example of Strong Induction An Example of Finding Closed Form Expression and Proof by Induction
Examples of Summations Euclidean Algorithm Example A Sample of a Proof of a GCD Fact
Examples of GCD Part 1 Examples of GCD Part 2 Divisors From Prime Factorization Example
Linear Diophantine Equation and EEA Example Congruent Iff Same Remainder Example
A Fermat's Little Theorem Example Congruence Equations
RSA Revisit CRT
Polar Coordinates Complex nth Roots
Fundamental Theorem of Algebra Long Division over $\mathbb{R}$ and $\mathbb{Z}_p$ Long Division over $\mathbb{R}$ and $\mathbb{Z}_p$ Part 2
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