Revised Notes are now in PDF Format and will be added as the year progresses. These notes are continuously being updated, and revised. If you spot any errors in these notes, please email the webmaster.
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Notes | Topic | Download |
1 |
Mathematical Induction Well-Ordering Principle Introduction to Primes |
PDF (new) |
2 |
Complete Mathematical Induction Problem with the Proof that everyone is the same age Series with Positive Terms: Convergence and Divergence Composite and Prime Numbers |
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3 |
Modular Arithmetic and Introduction to Congruences Basic Theorems (Congruences) Fundamental Theorem of Arithmetic |
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4 |
More Fundamental Theorem of Arithmetic Fermat's Little Theorem and Corollary Wilson's Theorem Euler's Function |
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5 |
Relatively Prime Numbers Euler's Theorem Introduction to Rational Numbers The Proof that Root 2 is Irrational |
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6 |
RSA Coding RSA Coding Example
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7 |
The Euclidean Algorithm
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8 |
Rational and Irrational Numbers |
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9 |
Irrational Numbers Algebraic Numbers Intermediate Value Theorem Upper and Lower Bounds |
PDF (new) |
10 |
Introduction to Real Numbers Real Number Thorems Dedekind Cuts |
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11 |
Complex Numbers |
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12 |
Fundamental Theorem of Algebra Proof Winding Numbers |
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13 |
Factor Theorem Size of Sets (Infinite and Finite) Introduction to Cardinality |
PDF (new) |
14 |
Cardinality Part I |
PDF (new) |
15 |
Cardinality Part II |
PDF (new) |
16 |
Cardinality Part III |
PDF (new) |
17 |
Cardinality Part IV Introduction to Compass and Straight Edge Problems |
PDF (new) |
18 |
Constructible Numbers Fields and Surds |
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19 |
Proof that one can not trisect an angle of 60 degrees with Compass and Straight Edge |
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20 |
Regular Polygons and Constructible Angles |
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21 |
More on Constructible Numbers, and Angles |
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22 |
Cardinality Aside (Very Short Notes ) |
PDF (new) |
23 |
Topology Part I |
PDF (new) |
Set Topology Handout |
HTML Format | |
24 |
Toplogy Part II |