Interdepartmental 301

Here is the syllabus, please show me it in class during the first week.

Here's my single favourite history of mathematics web site.

Here you may find a place to leave anonymous comments about the course.

Some comments about three reflections (includes as a particular case spin-reflections).

Here is a virtual slide rule.

Here's a place where you can make your own Julia sets. And a place to compare the Julia sets and the Mandelbrot set.

Here are some notes for proving the fundamental theorem of arithmetic.

Eventually there may be samples of final projects that aren't on sections that you'll be doing. There are - they are on the final project page.

The New York State regents exams you will be required to complete may be found here, from which you may select a wide variety of historical mathematics exams. One of your classmates found this one particularly interesting (from 1866). (I find the end-time of the first part particularly notable.)

This is the preparation guide for the New York State Mathematics Content Speciality Test. It provides a good summary of the mathematics that you will need to know. Pay particular attention to pages 7 - 14.

Here are some materials related to our work with polynomials:

Roots of Polynomials
Rational Root Theorem
Gauß's Lemma
Horner Scheme
A great detailed summary of all sorts of polynomial root theorems. Includes a proof (seven pages long!) of Descartes's rule of Signs. This is an excellent summary of our week on polynomial roots.
Newton's method you all (should) know for approximating real roots to polynomials. What about complex roots? A similar method is available - Laguerre's Method. Interesting and probably new to you as it was to me.

Here is a good website about the median-median line.

Here is an extremely short summary of NCTM Content Standards for INTD 301 Grades 6 - 12.

Numeration and Operations
    Rational Numbers
        Problem Solving
        Order
        Ratio & Proportions
    Number Theory
        Factors, Multiples, Primes, Relatively Prime
    Integers
    Complexes
    Vectors / Matrices
    Properties of Operations

Algebra
    Relations
    Functions (various representations)
        rates of change
        intercepts
        zeros
        asymptotes
        local / global
        arithmetic
        composition
        inversion
        exponential, polynomial, rational, logarithmic, periodic
    equivalent representations
    modeling

Geometry and Measurement
    properties/attributes of 2-3d
    problem solving - congruence & similarity, coordinates
    coordinates (cartesian, polar, spherical)
    transformations
    constructions
    area / volume formulae

Data Analysis / Probability
    make good graphics
    understand data and 'studies'
    display and calculate distributions
    run simulations
    use data and statistics to make predictions
    complementary, mutually exclusive, sample space
    expected value of random variables
    conditional probability and independent events
    compound events

Problem Solving
    Strategies, reflection and doing

Reasoning and Proof
    Conjecture and prove in various ways

Communication
    Discuss precisely

Connections
    Connect within and outside mathematics

Representation
    Represent in several ways

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