Victor M. Selby
Content Outline

Content Outline



Part l: Algebra 1

Chapter 1: The Power of Abstraction
    A). Defining whole numbers
    B). Pattern recognition and how generalization leads to
         axiom systems
    C). The inductive/deductive package
            1). Plan making: Upper-Paleolithic survival strategies
            2). The power of being numerate
Chapter 2: The Creative Mind
    A). Defining the rational numbers
    B). Introduction to Zeno’s paradox
    C). Discovering the laws of exponents
Chapter 3: Discovery
    A). Gaining a sense of the cosmos
            1). Scientific notation and the speed of light
            2). The light-year, space-time, and the size of
                 the universe
    B). The distributive pattern, negative numbers, and
         simplifying polynomials
Chapter 4: Balancing the World
    A). Solving for an unknown
    B). Variables as second-order abstractions
    C). Equations as models of the real world

Chapter 5: Functions
    A). Introduction to SETI and the Drake equation
    B). The spring function
    C). The pendulum and simple harmonic motion
    D). Defining the scientific method
            1). Descartes’ leap of imagination; mathematics
                 as the language of science
            2). Archimedes and the law of levers
            3). Longing for the harmonies and dealing
                 with the “irrational”
            4). Bucky Fuller and the concept of synergy

Chapter 6: Interdisciplinary Connections to Algebra l
    A). English: The power and creation of myth
    B). Social studies
            1). Plato’s allegory of the cave
            2). Greek culture and the rise of democracy
    C). Science: Greek astronomy, phases of the moon, and
         Ptolomy’s model of the heavens
    D). The Murth Game

Part ll: Geometry

Chapter 7: The Greek Mind
    A). The power of rational thinking
    B). The demands of space
            1). The Pythagorean theorem
            2). Symmetry and the nature of crystals
    C). From Thales to Euclid and the advent of
         Aristotelian logic
Chapter 8: Essential Proofs
    A). The axioms of Euclidian geometry
    B). From axioms to theorems; deductive power
            1). The supplementary angle theorem
            2). The vertical angle theorem
            3). If lines are parallel . . .
            4). Flat space and the sum of the angles of a
Chapter 9: A Journey into Curved Space
    A). Introduction to “Lineland, Flatland and
         Spaceland; analogy and mathematical models
    B). The fourth dimension
            1). Building the tesseract
            2). A visit from the oversphere
    C). Finite but unbounded space
            1). From lineland to circleland and from flatland
                 to sphereland
            2). Geodesics and the absence of parallels
            3). Curved space and the sum of the angles of
                 a triangle
            4). Einstein’s conception of a curved, 4-D
Chapter 10: Can’t Be but Must Be
    A). Indirect proofs
            1). Irrational numbers and a return to Zeno’s
            2). Cantor’s proof of larger orders of infinity
            3). Non-Euclidian geometries
    B). Unresolved paradoxes and self-referential
            1). Epimenides’ paradox
            2). Gödel’s theorem
Chapter 11: Deductive Power
    A). The amazing nine-point circle
    B). Limits and the derivation of formulas for area
         and volume of cones and spheres
    C). Ratios in similar objects and the connection to
Chapter 12: Think Deeply
    A). Changing assumptions; the nature of revolution
    B). Unifying the learning experience
Chapter 13: Student Geometry Work

Part lll: Algebra 2

Chapter 14: Planning Ahead
    A). The forebrain and cultural evolution
    B). Introduction to mathematics and the human
Chapter 15: Let the Games Begin
    A). Analysis and synthesis
    B). The “real” games
            1). Tic-Tac-Toe vs. Rock, Paper, Scissors
            2). Checkers vs. Undercut
            3). The Prisoner’s Dilemma and non-zero-sum
    C). The dollar auction and the cold war

Chapter 16: The Inductive Leap
    A). Generalizing sums of sequences
    B). Resolving Zeno’s paradox; limits are real
    C). Deriving the equations of the conic sections
    D). Galileo’s confirmation of the Copernican model
    E). Newton’s examination of instantaneous
Chapter 17: Challenging the Axioms
    A). Gravitation and curved space
    B). Relative time
Chapter 18: Models of Change
    A). Synergy vs. entropy; Bolzmann’s great idea
    B). The exponential function
            1). Population and compound growth
            2). Radioactive decay
    C). Darwin and Mendel; the how and why of
         physical evolution
Chapter 19: Imagination Unleashed
    A). Elements, alloys, and compounds; an essential
         look at analysis and synthesis
    B). Mendeleev’s chart, a classic example of the
         scientific method
    C). Imaginary numbers and modeling vectors
    D). The Gaussian curve and building a model of
         the atom
    E). The paradoxical quantum
Chapter 20: Mathematics and Morality
    A). Cooperation and defection as part of the
         human condition
    B). Humans as social critters; the ego dilemma
    C). Creating grand survival strategies; the role of
    D). The final project
Chapter 21: The Handout
Chapter 22: Student Algebra 2 Work

Part lV: A Model for Integration: Creating a department of
interdisciplinary studies

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