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An Invitation To Mathematics

Duration: 16:21:00
Lectures: 36
Level: Beginner

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This course is an introduction to the ideas and methods of mathematics. The only prerequisite is some familiarity with
topics in a typical high school mathematics curriculum. We will revisit many of these from a more conceptual viewpoint and
through numerous examples. Special emphasis will be laid on the interconnections between seemingly disjoint topics. This
course seeks to go beyond the “procedures-to-solve-routine problems” approach of a typical school curriculum to offer a
glimpse of what mathematics is really about. It should be suitable for high school students, lower undergraduates,
teachers at various levels, or others with a keen interest in mathematics.

1
An invitation to mathematics -Lec :01 -Introduction
16:31
2
An invitation to mathematics -Lec :02 -Long division
13:51
3
An invitation to mathematics -Lec :03 -Applications of Long division
14:30
4
An invitation to mathematics -Lec :04 -Lagrange interpolation
27:41
5
An invitation to mathematics -Lec :05 -The 0-1 idea in other contexts – dot and cross product
20:53
6
An invitation to mathematics -Lec :06 -Taylors formula
26:49
7
An invitation to mathematics -Lec :07 -The Chebyshev polynomials
28:15
8
An invitation to mathematics -Lec :08 -Counting number of monomials – several variables
24:46
9
An invitation to mathematics -Lec :09 -Permutations, combinations and the binomial theorem.
29:34
10
An invitation to mathematics -Lec :10 -Combinations with repetition, and counting monomials.
20:36
11
An invitation to mathematics -Lec :11 -Combinations with restrictions, recurrence relations
26:48
12
An invitation to mathematics -Lec :12 -Fibonacci numbers; an identity and a bijective proof.
20:41
13
An invitation to mathematics -Lec :13 -Permutations and cycle type
28:05
14
An invitation to mathematics -Lec :14 – The sign of a permutation, composition of permutations
37;09
15
An invitation to mathematics -Lec :15 -Rules for drawing tangle diagrams
17:56
16
An invitation to mathematics -Lec :16 -Signs and cycle decompositions
21:05
17
An invitation to mathematics -Lec :17 -Sorting lists of numbers, and crossings in tangle diagrams
18:02
18
An invitation to mathematics -Lec :18 -Real and integer valued polynomials
18:03
19
An invitation to mathematics -Lec :19 -Integer valued polynomials revisited.
25:20
20
An invitation to mathematics -Lec :20 -Functions on the real line, continuity
22:52
21
An invitation to mathematics -Lec :21 -The intermediate value property.
35:09
22
An invitation to mathematics -Lec :22 -Visualizing functions.
27:53
23
An invitation to mathematics -Lec :23 -Functions on the plane, Rigid motions.
24:44
24
An invitation to mathematics -Lec :24 -More examples of functions on the plane, dilations.
29:07
25
An invitation to mathematics -Lec :25 -Composition of functions
27:51
26
An invitation to mathematics -Lec :26 – Affine and Linear transformations
32:22
27
An invitation to mathematics -Lec :27 -Length and Area dilation, the derivative
28:03
28
An invitation to mathematics -Lec :28 -Examples-I
25:03
29
An invitation to mathematics -Lec :29 -Examples-II
20:58
30
An invitation to mathematics -Lec :30 -Linear equations, Lagrange interpolation revisited
28:56
31
An invitation to mathematics -Lec :31 -Completed Matrices in combinatorics
28:51
32
An invitation to mathematics -Lec :32 -Polynomials acting on matrices
26:44
33
An invitation to mathematics -Lec :33 -Divisibility, prime numbers
21:03
34
An invitation to mathematics -Lec :34 -Congruences, Modular arithmetic
24:52
35
An invitation to mathematics -Lec :35 -The Chinese remainder theorem
27:22
36
An invitation to mathematics -Lec :36 -The Euclidean algorithm, the 0-1 idea and the Chinese remainder theorem
27:38

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An Invitation To Mathematics
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