Mathematics Content Defense
CRISPIN A E STROMBERG
Background
Master of Science, Applied Statistics
◦ Kennesaw State University, 2012
Graduate Mathematics and Statistics Courses
◦ University of West Florida
Bachelor of Science, Mathematics
◦ University of North Georgia, 2010
Mathematics Instructor
◦ Lanier Technical College
◦ Lifelong Education Opportunities
Mathematics Tutor
◦ Georgia State University
◦ Private
Self-Assessment Tools
Practice GACE Missed:
1 Number & Quantity, 2 Algebra, 2 Discrete Math, 1 Calculus, 1 Function, 3 Geometry, 0 Prob/Stats
Self Assessment
◦ All Areas Need Some Review
 Number and Quantity
 Algebra
 Discrete Mathematics and Calculus
 Functions
 Geometry
 Probability and Statistics
AREA I: Number and Quantity
There are a few outcomes that will require review, and I can do this on my own.
Study Plan for Number and Quantity
Review vector addition operations, velocity problems, polar coordinate representations of complex
numbers, and complex number operations in the plane.
TEXT: Chapter 8, sections 2, 3 and 4 of Precalculus: An Investigation of Functions by David Lippman and
Melonie Rasmussen (2014).
This will be completed by September 30th, 2015.
AREA I: Number and Quantity
Evidence to Support Plan
Coursework
•
•
•
•
Precalculus
Calculus Sequence
Real Analysis (undergraduate and graduate)
Physics I and II
Teaching/Tutoring
• College-level Learning Support Math
• Algebra I and II
AREA II: Algebra
There are a few outcomes that will require review, and I can do this on my own.
Study Plan for Algebra
I will review the binomial theorem, rate of change, and techniques for analyzing zeros of functions.
I will accomplish this by reading and working problems in extended Chapter 3, sections 1 through 5 of
Precalculus: An Investigation of Functions by David Lippman and Melonie Rasmussen (2014).
This will be accomplished by September 30th, 2015.
AREA II: Algebra
Evidence to Support Plan
Coursework
• Precalculus
• Calculus Sequence
• Real Analysis (undergraduate and graduate)
Teaching/Tutoring
• College-Level Learning Support math classes
• Algebra I and II
AREA III: Discrete Mathematics and Calculus
There are a few outcomes that will require review, and I can do this on my own.
Study Plan for Discrete Mathematics and Calculus
I will review sequences, basic vertex-edge graphs, trees, and networks, truth statements, one-sided and
non-existent limits, continuity tests, behavior of functions, applications of the calculus, and infinite series.
I will study and work problems in Chapters 3,6,8,9, and 10 in Applied Discrete Structures by Alan Doerr and
Kenneth Levasseur (2013). For the calculus areas, I will study and work problems in Chapters 1,3,4,7, and 8
of the APEX book, Calculus, by Gregory Hartman, Brian Heinold, Troy Siemers, and Dimplekumar
Chalishajar (2013).
Chapter Contents
This will be completed by November 30th, 2015.
AREA III: Discrete Mathematics and Calculus
Applied Discrete Structures by Alan Doerr and Kenneth Levasseur
Applied Discrete Structures
Chapters 3, 6, 8, 9, 10
Calculus, by Gregory Hartman, Brian Heinold, Troy Siemers, and Dimplekumar Chalishajar
Calculus
Chapters 1, 3, 4, 7, 8
AREA III: Discrete Mathematics and Calculus
Evidence to Support Plan
Coursework
• Discrete Mathematics
• Calculus Sequence
• Differential Equations
• Partial Differential Equations (graduate)
• Mathematical Modeling (graduate)
• Real Analysis (undergraduate and graduate)
Tutoring
• Calculus Sequence
AREA IV: Functions
There are a few outcomes that will require review, and I can do this on my own.
Study Plan for Functions
I will review inverse functions to solve trigonometric equations in modeling contexts.
This will be accomplished by reading and working problems in Chapter 6, sections 3-5 of Precalculus: An
Investigation of Functions by David Lippman and Melonie Rasmussen (2014).
This will be completed by September 30th, 2015.
AREA IV: Functions
Evidence to Support Plan
Coursework
• Precalculus
• Calculus Sequence
• Real Analysis (undergraduate and graduate)
Teaching/Tutoring
• Algebra I and II
• Trigonometry
AREA V: Geometry
There are a few outcomes that will require review, and I can do this on my own.
Study Plan for Geometry
I will review compass and straightedge constructions, congruence in terms of rigid motions, equations of
conic sections with foci given, circle theorems, sectors of circles, and geometric methods to solve design
problems.
I will accomplish this by reading and working problems in Chapters 2-4 of College Geometry Using the
Geometer’s Sketchpad by Barbara E. Reynolds and William E. Fenton.
If schedule permits, I will also take Modern Geometry when it is offered in the Spring semester of 2016.
This will be completed by May 15th, 2016.
AREA V: Geometry
Evidence to Support Plan
Coursework
• Modern Geometry (Undergraduate)
Teaching/Tutoring:
• Geometry
• Algebra II
• Trigonometry
AREA VI: Probability and Statistics
There are a few outcomes that will require review, and I can do this on my own.
Study Plan for Probability and Statistics
I will review Probability Distributions, Expected Value, and Simulations. I will do this by studying:
Chapter 2: Probability
Chapter 3: Random Variables
in An Introduction to Mathematical Statistics.
This will be completed by May 15th, 2016.
AREA VI: Probability and Statistics
Evidence to Support Plan
Coursework
• Mathematical Statistics I (grad)
• Mathematical Statistics II (grad)
• M.S. in Applied Statistics
Work Experience
• Statistics Internship
Texts
Doerr, A. & Levasseur, K. (2013). Applied Discrete Structures. Retrieved from:
http://faculty.uml.edu/klevasseur/ADS2_zips/ADS_V2-0.pdf
Hartman, G., Heinold, B., Siemers, T., & Chalishajar, D. (2013). Calculus. J. Bowen (Ed.). Retrieved from:
http://www.vmi.edu/WorkArea/DownloadAsset.aspx?id=10737424884
Larsen, R.& Marx, M. (2005). An Introduction to Mathematical Statistics (4th ed.). Prentice Hall.
Lippman, D.& Rasmussen, M., (2014). Precalculus: An Investigation of Functions. Retrieved from
http://www.opentextbookstore.com/precalc/1.4/Precalc.pdf
Reynolds, B. & Fenton, W. ( 2012). College Geometry using the Geometer’s Sketchpad. Sommerset. NJ: Wiley.
Online Resources
NPTEL
Khan Academy
YouTube
Coursework
Title of Course
Listing
Date
Level
Institution
Title of Course
Listing
Date
Level
Institution
Numerical Analysis I
MAD 6405
Spring 2015
Graduate
UWF
Senior Project in Math
MATH 4950
Fall 2010
Undergrad.
UNG
Real Analysis
MAA 6306
Fall 2014
Graduate
UWF
Intro to Discrete Mathematics
MATH 3500
Fall 2010
Undergrad.
UNG
Mathematical Statistics II
STA 5326
Summer 2014
Graduate
UWF
Differential Equations
MATH 3000
Fall 2010
Undergrad.
UNG
Partial Differential Equations
MAP 5345
Summer 2014
Graduate
UWF
Game Theory
MATH 3950
Spring 2010
Undergrad.
UNG
Mathematical Modeling
MAP 6108
Spring 2014
Graduate
UWF
History of Mathematics
MATH 4700
Spring 2010
Undergrad.
UNG
Biostatistics
STA 5176
Fall 2013
Graduate
UWF
Adv Calculus I (Real Analysis)
MATH 4661
Fall 1998
Undergrad.
GSU
Matrix Theory
MAS 5145
Fall 2013
Graduate
UWF
Advanced Probability
MAP 5471
Summer 2011
Graduate
UWF
Modern Algebra I
MATH 4441
Spring 1999
Undergrad.
GSU
Applied Analysis Project
STAT 8940
Fall 2012
Graduate
KSU
Geometry
MATH 3120
Summer 1999
Undergrad.
GSU
Applied Categorical Data Analysis
STAT 8310
Fall 2012
Graduate
KSU
Intermediate Linear Algebra
MATH 435
Winter 1997
Undergrad.
GSU
Advanced Programming in SAS
STAT 8020
Fall 2012
Graduate
KSU
Mathematical Statistics I
MATH 451
Winter 1997
Undregrad.
GSU
Applied Analysis Project
STAT 8940
Summer 2012
Graduate
KSU
Intro Linear Algebra
MATH 335
Fall 1996
Undergrad.
GSU
Applied Regression Analysis
STAT 8210
Summer 2012
Graduate
KSU
Discrete Mathematics
MATH 220
Winter 1996
Undergrad.
GSU
Applied Experimental Design
STAT 8120
Spring 2012
Graduate
KSU
Intermediate Calculus
MATH 214
Winter 1996
Undergrad.
GSU
Programming in R
STAT 7900
Spring 2012
Graduate
KSU
Multivariable Calculus III
MATH 213
Fall 1995
Undergrad.
GSU
Statistical Methods
STAT 7100
Fall 2011
Graduate
KSU
Calculus of One Var II
MATH 212
Summer 1995
Undergrad.
GSU
Statistical Computing
STAT 7000
Fall 2011
Graduate
KSU
Calculus of One Var I
MATH 211
Spring 1995
Undergrad.
GSU
PreCalculus
MATH 126
Winter 1995
Undergrad.
GSU