Ken Monks
    Dept. of Mathematics
    University of Scranton
    Scranton, PA 18510
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Syllabus of Topics

Math 104 - Mathematics for Elementary Teachers
University of Scranton

Lecture Topics - Overview

Each of the 28 topics listed here represent approximately one lecture's worth of material. The remainder of the class meetings will be used for exams, reviews, additional topics provided by the instructor, and extra time to go over topics that require more than one lecture to cover.

  1. Patterns and Sequences
  2. Sets and set operations
  3. Functions
  4. Logic
  5. Natural Numbers
  6. Addition and Subtraction of Natural Numbers
  7. Multiplication of Natural Numbers
  8. Division and Exponents for Natural Numbers
  9. Divisibility
  10. Primes, GCD, LCM
  11. Integers
  12. Rational Numbers
  13. Rational Arithmetic
  14. Decimal Notation
  15. Ratio, Percent, Scientific Notation
  16. Real Numbers and Irrational Numbers
  17. Algebraic Expressions, Equations, Inequalities
  18. Functions and their Graphs
  19. Probability - Single Stage Experiments
  20. Probability - Multistage Experiments
  21. Plane Geometry
  22. Polygons and Tessellations
  23. Three Dimensional Geometry
  24. Symmetry, Rotation, Reflection
  25. Measurements and Units
  26. Area and Perimeter
  27. Volume and Surface Area
  28. Congruence and Constructions

Topics Covered - Details

  1. Patterns and Sequences
    1. sequences
      1. finite sequences
      2. infinite sequences
    2. periodic sequences
    3. arithmetic sequence
    4. geometric sequence
    5. method of differences
    6. other sequences (e.g. Fibonacci)
  2. Sets and set operations
    1. elements and membership
    2. finite sets and notation
    3. infinite sets and set builder notation
    4. set equality and subsets
    5. set operations
      1. union
      2. intersection
      3. difference
      4. complement
      5. Cartesian product
    6. Venn diagrams
  3. Functions
    1. definition
    2. representation
      1. as a rule
      2. as a table
      3. as a graph
      4. as Venn-like diagrams
  4. Logic
    1. statements
    2. deduction and proof
    3. conditional statements
      1. definition
      2. converse
      3. inverse
      4. contrapositive
    4. negation
    5. rules of inference
      1. modus ponens
      2. contraposition
    6. logical operators: and, or, not, implies, if and only if
    7. Venn diagram approach to statements with quantifiers
  5. Natural Numbers
    1. base n representation of natural numbers
    2. conversion between bases
    3. other representations: Roman numerals, Mayan numerals
  6. Addition and Subtraction of Natural Numbers
    1. properties
      1. closure
      2. commutativity
      3. associativity
      4. identity
    2. definition of inequality
    3. subtraction
      1. definition
      2. properties
    4. algorithms for addition and subtraction in base n
    5. estimation
  7. Multiplication of Natural Numbers
    1. definition
    2. properties
      1. closure
      2. commutativity
      3. associativity
      4. identity
      5. distributive
    3. algorithms for multiplication in base n
    4. estimation
  8. Division and Exponents for Natural Numbers
    1. The Division Theorem (a=bq+r)
    2. definition and notation for division
    3. exponents
      1. definition
      2. laws of exponents
    4. precedence of operations
  9. Divisibility
    1. definition of a|b
    2. definition of even and odd
    3. properties of |
    4. definition of prime number
    5. Sieve of Eratosthenes
    6. tests for divisibility by 2,3,4,5,6,7,8,9,10,11
    7. testing a number to see if it is prime
  10. Prime factorization, GCD, LCM
    1. Fundamental Theorem of Arithmetic
      1. finding the prime factorization
        1. by factor tree
    2. GCD
      1. definition
      2. computing GCD(a,b)
        1. by listing divisors
        2. by prime factorization
        3. by the Euclidean algorithm
    3. LCM
      1. definition
      2. computing LCM(a,b)
        1. by listing multiples
        2. by prime factorization
        3. by the Euclidean algorithm with LCM(a,b)=ab/GCD(a,b)
  11. Integers
    1. definition of additive inverse or opposite
    2. addition of integers
    3. subtraction of integers
    4. multiplication of integers
    5. properties of integer arithmetic
    6. division of integers
    7. definition of inequality of integers
  12. Rational Numbers
    1. definition of fraction
    2. equality of fractions
      1. reducing fractions
      2. cross multiplication
    3. rules for signs in fractions
    4. inequality of fractions
      1. cross multiplication
    5. mixed numbers
    6. improper fractions
  13. Rational Arithmetic
    1. addition, subtraction, multiplication, and division of fractions
    2. arithmetic with natural numbers and fractions
    3. negative exponents
    4. properties of rational arithmetic
  14. Decimal Notation
    1. definition: place value in base n
    2. finite decimals and repeating decimals
    3. criteria for a fraction to have a finite decimal
    4. converting a fraction to a repeating decimal
    5. converting a repeating decimal to a fraction
  15. Ratio, Percent, Scientific Notation
    1. ratio notation (a:b
    2. definition of proportion
    3. definition of %
    4. scientific notation
    5. word problems
  16. Real Numbers and Irrational Numbers
    1. definition irrational
    2. Pythagorean theorem
    3. irrationality of sqrt(2)
    4. definition of nth-roots
    5. product of two square roots
    6. properties of real arithmetic
  17. Algebraic Expressions, Equations, Inequalities
    1. simplifying algebraic expressions
    2. solving linear equations in one variable
    3. solving linear inequalities in one variable
      1. plotting the solution on a number line
    4. substitution
  18. Functions and their Graphs
    1. linear functions: f(x)=mx+b
      1. slope
      2. intercept
      3. point-point formula for slope
    2. step functions
    3. quadratic function
    4. exponential functions
      1. doubling: 2x
      2. compound interest: ex
  19. Probability - Single Stage Experiments
    1. probability of an event in a finite sample space
    2. probability of mutually exclusive events (addition property)
    3. probability of a non-mutually exclusive events (two events only)
    4. definition of odds
    5. experimental probabilities and simulations
  20. Probability - Multistage Experiments
    1. probability if independent events (multiplication property)
    2. tree diagram for multistage experiments
    3. probability of complementary events
    4. expected value
  21. Plane Geometry
    1. basic terms: point, line, plane, ray, segment, half-plane, angle, collinear, coplanar
    2. angle measurement (degrees, minutes, seconds)
    3. types of angles
      1. acute
      2. obtuse
      3. right
    4. relationships among angles
      1. supplementary
      2. complementary
      3. adjacent
      4. vertical
    5. relationships among lines
      1. perpendicular
      2. parallel
        1. alternate interior angle theorem
    6. simple closed curves and convex sets
    7. circles
      1. definition
      2. basic terms: radius, diameter, chord, tangent
    8. polygons
    9. types of polygons
  22. Polygons and Tessellations
    1. sum of the angle measures in convex polygons
    2. congruence of line segments and angles
    3. regular polygons
    4. tessellations
      1. regular
      2. semi-regular
      3. with congruent tiles which are not regular
  23. Three Dimensional Geometry
    1. polyhedra
      1. regular polyhedra
      2. semi-regular polyhedra
    2. pyramids and right pyramids
    3. prisms and right prisms
    4. cones and cylinders
    5. spheres
      1. maps
        1. latitude
        2. longitude
  24. Symmetry, Rotation, Reflection
    1. symmetry in the plane
      1. reflection: lines of symmetry
      2. rotational symmetry about a point
    2. symmetry in 3-space
      1. reflection: planes of symmetry
      2. rotational symmetry about a line
  25. Measurements and Units
    1. English units: length, area, volume, mass, temperature
    2. metric units: length, area, volume, mass, temperature
    3. converting between units
  26. Area and Perimeter
    1. squares
    2. triangles
    3. parallelograms and rectangles
    4. trapezoids
    5. circles
  27. Volume and Surface Area
    1. right prisms
    2. cylinders
    3. pyramids
    4. cone
    5. sphere
  28. Congruence and Constructions
    1. definition of congruence for polygons
    2. ruler and compass constructions
      1. congruent segments
      2. congruent angles
      3. congruent triangle (by SSS theorem)
      4. perpendicular bisector
      5. angle bisector
      6. perpendicular to a line through a given point
      7. circumscribed circle about a triangle
      8. a line parallel to a given line through a point not on the given line
    3. the triangle inequality
    4. ASA, SAS, SSS, AAS theorems
 

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This page was last  updated on Sunday, May 28, 2000 12:32:12 AM. © Ken Monks