Sample Syllabus (Core Curriculum)
Field Topic Units: Mathematics
One (1) Topic Unit = One (1) 20- to 30- minute Lecture
So, a 3 credit hour class would be 9 Topic Units per week,
and a 16 week semester would consist of 144 Topic Units.
Depending on the nature of the class and subject matter, for some subjects, students may elect to take only some of the Topic Units for a class, or they may choose to take all of them while they learn at their own pace.
Professors: TBA (with contact information)
Office Hours: TBA
Course Description: Topic Units are organized by subject. A Field Topic Unit is an overarching subject that encompasses many more specialized subjects in the field. For example, the Field Topic of Mathematics includes Advanced Algebra, Geometry, Trigonometry, Calculus, Statistics, and more.
Graduation Requirements for Field Topic Units:
Minimum For All Students:
30 Topic Units in Psychology
50 Topic Units in Mathematics
50 Topic Units in Sciences
50 Topic Units in English Language and Literature
30 Topic Units in History
Students with Professional Applications related to given subject area(s) are required to take more Topic Units in those areas (i.e. a student utilizing a significant amount of mathematical formulas and/or skills in his project must take at least 120 Topic Units in Mathematics).
After each Topic Unit, students will take a Topic Assessment. Assessments are computer-based, closed-book exams that are tested to a statistical proficiency level rather than graded on a traditional A-F scale. Students need a minimum of 90% correct answers on a Topic Assessment to pass.
Topic Unit # Lecture Title
A01 Advanced Algebra - Intro and Basics
A02 Polynomial Functions
A05 Data Analysis
A06 Roots and Radicals
A07 Quadratic Functions
A08 3-Variable Equation Systems
A09 Rational Equations
A10 Systems of Inequalities
A12 Real-World Application Part 1
A13 Real-World Application Part 2
A14 Abstract Algebra
A15 Universal Algebra
A16 Normed Linear Spaces
A17 Banach Spaces
A18 Hilbert Spaces
A19 Topological Groups
G01 Geometry - Intro and Basics
G02 Creating Proofs
G03 Lines and Linear Equations
G05 Congruence and Similarity
G06 Determining Surface Area
G07 Determining Volume
G08 Determining Mass
G09 Properties of Triangles
G10 Types of Triangles
G11 Calculations With Triangles
G12 Real-World Applications With Triangles
G13 Concave Polygons
G14 Convex Polygons
G15 Circles and Spheres
G16 Calculations with Circles
G17 Calculations with Spheres
G18 Parallel Lines
G20 Properties of Quadrilaterals
G21 Types of Quadrilaterals
G22 Calculations With Quadrilaterals
G23 Real-World Applications With Quadrilaterals
T01 Trigonometry - Intro and Basics
T02 Intro to the Six Basic Trigonometric Functions
T03 The Sine
T04 The Cosine
T05 The Tangent
T06 The Secant
T07 The Cosecant
T08 The Cotangent
T09 Verifying Trigonometric Identities
T10 Graphing Trigonometric Functions
T11 Law of Sines
T12 Law of Cosines
T13 Formulas for Area of Triangles
T14 Vector Addition and Scalar Multiplication
T15 Rectangular and Polar Coordinates
T16 The Dot Product
T17 Complex Numbers
T18 Addition and Subtraction Formulas
T19 Multiple Angle Formulas
T20 Real-World Trigonometry Application Part 1
T21 Real-World Trigonometry Application Part 2
P01 Pre-Calculus - Intro and Basics
P02 Linear Function Review
P03 Quadratic Equation Review
P04 Polynomial Review
P06 Dividing Polynomials
P08 Rational and Real Exponents
P09 Logarithms and Inverses of Exponents
P10 Properties of Logarithms
P12 Approximating Area Under A Curve
P13 Unit Circles
P14 Negative Angles
P15 Computing Circular Arc Length
P17 Converting Radians to Degrees
P19 Trigonometric Function Review Part 2
P20 Right Triangle Review
P22 Inverse Trigonometric Function Review Part 2
P23 Double-Angle Formulas
P24 Half-Angle Formulas
P25 Addition and Subtraction Formulas
P26 Polar Coordinate Review
P27 Real-World Precalculus Applications
C01 Calculus - Intro and Basics
C02 Basic Differentiation Rules - Intro
C03 Basic Integration Formulas - Intro
C04 Functions and their Graphs
C05 FItting Models to Data Graphs
C06 What Are Limits?
C07 How To Find and Evaluate Limits
C08 Types of Limits
C09 Infinite Limits
C10 Differentiation and Derivatives
C11 Real-World Application of Derivatives
P01 Classical Mechanics - Intro and Basics
C12 The Product Rule
C15 The Chain Rule
C16 Rolle’s Theorem
C18 Curve Sketching
C19 Newton’s Method
C21 Riemann Sums
C24 Real-World Application of Integrals
CE01 Civic Engineering - Intro and Basics
C25 e and the ln function
C26 Differential Equations
C28 Inverse Functions
C29 Integration and Volume
C30 Integration and Area
C32 Parametric Equations
C33 Graphing Polar Coordinates
C34 Working With Vectors - Intro
C35 Vectors and Differentiation
C36 Vectors and Integration
C37 Tangent Vectors
C38 Real-World Applications of Vectors
C39 Working With Several Variables - Intro
C40 Chain Rule
C46 Stokes’ Theorem
S01 Statistics - Intro and Basics
S02 Statistical Formulas Part 1
S03 Statistical Formulas Part 2
S04 Data Relationships
S05 Data Inferences
S07 Probability and Randomness
S08 Statistical Sampling
S09 Inference - Intro
S10 Statistical Regression
S11 Multiple Regression
S12 One-Way Variance Analysis
S13 Two-Way Variance Analysis
S14 Parametric Tests
S15 Nonparametric Tests
S16 Statistical Applications in Science
S17 Statistical Applications in Medicine
S18 Statistical Applications in Psychology
S19 Statistical Applications in Sociology
S20 Statistical Applications in Engineering
S21 Statistical Applications in Business
S22 Statistical Applications in Economics
Students may choose from our suggested resources in order to get a better grasp on their understanding of Topic Unit material in addition to listening to Lecture material, or they may also look for additional resources on their own. This list is to be viewed as a starting point, not as comprehensive.
Related resources do not have a one-to-one Topic Unit correlation, although certain resources do tend to apply more to certain Topic Units.
Birkhoff, G. & MacLane, S. (1998). A Survey of Modern Algebra. London: A.K. Peters.
Lial, M., Hornsby, J., Schneider, D. II., & McGinnis,M. (2009). Essentials of College Algebra. Boston: Addison-Wesley.
Jacobs, R. (2003). Geometry: Seeing, Doing, Understanding. New York: W. H. Freeman.
Rhoad, R., Milauskas, G., & Whipple, R. (1991). Geometry for Enjoyment and Challenge. Boston: McDougal Littell/Houghton-Mifflin.
Larson, Ron & Hostetler, Robert P. (2010). Trigonometry. Independence, KY: Cengage Learning.
McKeague, Charles D. & Turner, Mark P. (2007). Trigonometry. Belmont, CA: Brooks-Cole.
Cohen, D., Lee, T., & Sklar, J. (2011). Precalculus (7th ed.). Belmont, CA: Brooks-Cole.
Dugopolski, Mark. (2008). Precalculus: Functions and Graphs (3rd ed.). Boston: Addison-Wesley.
Simmons, George. (2003). Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry. Eugene, OR: Wipf & Stock.
Larson, R. & Edwards, Bruce H. (2009). Calculus. Independence, KY: Cengage Learning.
Stewart, James. (2011). Calculus. Belmont, CA: Thomson Brooks-Cole.
Kokoska, Stephen. (2010). Introductory Statistics: A Problem-Solving Approach. New York: W.H. Freeman.
Triola, Mario F. (2010). Essentials of Statistics (4th ed.). Upper Saddle River, NJ: Pearson Education.
Online statistics book list: http://www.meandeviation.com/tutorials/stats/notes/booklist.html