# Class Notes for Mathematics at University of Waterloo (UW)

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UWMATH135Shane BaumanFall

## MATH135 Lecture 1: Introduction

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All course information can be found on learn. Assignments are due every wednesday at 8:25am and are to be submitted electronically through crowdmark. A
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UWMATH135Shane BaumanFall

## MATH135 Lecture 15: More POMI and POSI

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UWMATH135Shane BaumanFall

## MATH135 Lecture Notes - Lecture 2: Angle

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Math 135 - lecture 2: introduction to proofs. Proposition a statement that needs to be proven true or demonstrated false by a valid argument. Lemma a p
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UWMATH135Shane BaumanFall

## MATH135 Lecture Notes - Lecture 5: Empty Set, Asteroid Family, Cartesian Coordinate System

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Math 135 - lecture 5: more divisibility and introduction to sets. Let a, b, and c be integers. If a | b and a | c then for any integers x and y, a | (b
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UWMATH127Keegan KeplingerFall

## MATH127 Lecture Notes - Lecture 1: Real Number, Venn Diagram

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Integers (symbolized as z) any number from - to + that can be written without a fractional component. Natural numbers (symbolized as n) any number grea
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UWMATH135Shane BaumanFall

## MATH135 Lecture Notes - Lecture 7: Open Formula, Mathematical Object, Natural Number

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Math 135 - lecture 7: universal and existential quantifiers: No, it is sometimes true and sometimes false depending on the variable x. If something dep
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UWMATH135Shane BaumanFall

## MATH135 Lecture Notes - Lecture 6: Disjoint Sets, If And Only If, Subset

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Math 135 - lecture 6: subsets, set equality, converse, and iff. Disjoint sets: s and t are said to be disjoint sets when s t = . Subsets: a set s is ca
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UWMATH135Shane BaumanFall

## MATH135 Lecture Notes - Lecture 16: Natural Number

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UWMATH127Keegan KeplingerFall

## MATH127 Lecture 2: Review

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UWMATH135Shane BaumanFall

## MATH135 Lecture Notes - Lecture 4: Immunoglobulin Light Chain, Junkers D.I, Gallium

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Math 135 - lecture 4: more implication and divisibility. B, as shown in the truth table above. Therefore, we can find the negation of an implication: I
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UWMATH135Shane BaumanFall

## MATH135 Lecture Notes - Lecture 22: Integer Factorization, If And Only If

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Math 135 - lecture 22: pad, uft, and dfpf. Pad is referred to as a corollary of cad. If p is prime and p | (m1m2,,mn) for integers m1, m2,,mn then p |
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UWMATH135Shane BaumanFall

## MATH135 Lecture Notes - Lecture 30: Prime Number, Chinese Remainder Theorem

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