MATH2101 College Algebra 

COURSE PREVIEW AND SYLLABUS

COURSE DESCRIPTION 

This course provides a survey of college-level algebra for non-STEM majors. The primary topics involve understanding and applying key properties of common functions including linear, polynomial (including those representing conic sections), rational, exponential, and logarithmic. Additional topics include designing and solving systems of linear equations, observing and understanding patterns represented by sequences and series, and an introduction to using mathematics as a tool for deductive reasoning. Each topic will be motivated by and applied to historical and/or practical applications. The course is designed to equip the Learner with an understanding of, appreciation for, and ability to confidently use the language of algebra as a tool in transformative learning and leadership. 

COURSE FACULTY

Jeffrey R. Christianson, Ph.D

 

COURSE OUTLINE

Module 1: Foundations of Algebra 

College Algebra (1.1 – 1.6, 2.1 – 2.7) 

Problem Set #1 

Module Assessment #1 

Journal Question #1 

 

What is algebra and why is it useful? Upon successful completion of this module, the Learner will be able to define and explain the importance of algebra and will demonstrate both practical proficiency with and a worldview-informed understanding of fundamental concepts of high-school-level arithmetic and algebra including real and complex numbers, the Cartesian coordinate system, exponents, radicals, basic operations on polynomial and rational expressions, linear and quadratic equations, and linear and absolute value inequalities. 

 

Module 2: Functions 

College Algebra (3.1 – 3.7, 4.1) 

Problem Set #2 

Module Assessment #2 

 

What are functions and why are they useful? Upon successful completion of this module, the Learner will be able to define, explain the importance of, and demonstrate practical proficiency with functions and their properties including notation, domain and range, average rates of change, composition, transformation, and inverse. The specific examples of linear and absolute value functions will be examined more closely. 

 

Module 3: Polynomial Functions 

College Algebra (5.1 – 5.4) 

The Dance of Number (14.1 – 14.3) 

Problem Set #3 

Module Assessment #3 

 

What are polynomial functions and why are they useful? Upon successful completion of this module, the Learner will be able to define, explain the importance of, and demonstrate practical proficiency with polynomial functions and their properties including defining characteristics, zeros, end behavior, and divisibility. 

 

Module 4: Rational Functions and Finding Zeros of Polynomial Functions 

College Algebra (5.5 – 5.8) 

Problem Set #4 

Module Assessment #4 

Journal Question #2 

 

What is the meaning and relevance of zeros of polynomial and rational functions? Upon successful completion of this module, the Learner will be able to explain the importance of and demonstrate proficiency investigating zeros of and graphing polynomial and rational functions using the Remainder, Factor, Rational Zero, and Conjugate Pairs theorems. 

 

Module 5: Exponential and Logarithmic Functions 

College Algebra (6.1 – 6.6) 

The Dance of Number (12.1 – 12.5) 

Problem Set #5 

Module Assessment #5 

 

What are exponential and logarithmic functions and why are they useful? Upon successful completion of this module, the Learner will be able to define, explain the importance of, and demonstrate practical proficiency with the number e and exponential and logarithmic functions and their properties including their graphical nature and algebraic operations. 

 

Module 6: Systems of Equations and Inequalities 

College Algebra (7.1 – 7.4) 

Problem Set #6 

Module Assessment #6 

 

What are systems of equations and why are they useful? Upon successful completion of this module, the Learner will be able to define, explain the importance of, and demonstrate practical proficiency with setting up, evaluating solvability, and solving systems of linear and quadratic equations and inequalities using methods such as substitution, addition, and elimination. 

 

Module 7: Matrices and Solving Linear Systems of Equations 

College Algebra (7.5 – 7.8) 

Problem Set #7 

Module Assessment #7 

Journal Question #3 

 

What are matrices and why are they useful? Upon successful completion of this module, the Learner will be able to define, explain the importance of, and demonstrate practical proficiency with matrices, matrix operations including addition, subtraction, and multiplication, and representing systems of linear equations as matrices and solving them using Gaussian elimination, matrix inversion, and Cramer’s Rule. 

 

Module 8: Conic Sections 

College Algebra (8.1 – 8.4) 

The Dance of Number (13.8) 

Problem Set #8 

Module Assessment #8 

 

What are conic sections and why are they useful? Upon successful completion of this module, the Learner will be able to define, explain the importance of, and demonstrate practical proficiency with equations, graphs, and properties of circles, ellipses, parabolas, and hyperbolas. 

 

Module 9: Sequences and Series 

College Algebra (9.1 – 9.4) 

Problem Set #9 

Module Assessment #9 

 

What are sequences and series and why are they useful? Upon successful completion of this module, the Learner will be able to define, explain the importance of, and demonstrate practical proficiency with arithmetic and geometric sequences and series, including writing and using recursive and explicit formulae and finding sums of finite and convergent infinite series. 

 

Module 10: Mathematical Reasoning 

The Dance of Number (13.1 – 13.3, 13.9) 

Problem Set #10 

Module Assessment #10 

Journal Question #4 

Course Assessment 

 

What is mathematical reasoning and why is it useful? Upon successful completion of this module, the Learner will be able to explain the place and limitations of reasoning in mathematics and demonstrate practical proficiency with basic methods of direct and indirect proofs. 

 

COURSE RESOURCES

Required Texts:

• Abramson, Jay et al. College Algebra (Houston, TX: OpenStax, 2017), ISBN: 1938168380, https://openstax.org/books/college-algebra/pages/1-introduction-to-prerequisites, Free Online (open source, hard copy retail: $52), sections as specified for each module. 

• Nickel, James D. The Dance of Number: Dance Moves – Mastering Algebra and Mathematical Reasoning, Part 2, Volume 2 (Wenatchee, WA: Sound Mind Press, 2018), ISBN 9780999105474, Retail: $55), sections as specified. [Available to rent from the Agathon Research Library] 

LEARNING OUTCOMES

 

Course Learning Outcomes (CLOs)

1. Demonstrate an intuitive understanding of the language of algebra (CBULO 1, 2, BPCO 1). 
2. Apply this understanding to define and solve practical problems (CBULO 2, 3, BPCO 2, APCO 1). 
3. Analyze mathematical reasoning and thought within the context of worldview considerations (CBULO 4, 5, BPCO 3, 4, APCO 2, 3). 

Program Learning Outcomes (PLOs)

PLOs for A. Ed:  

1. To prepare Learners for specialized undergrad study in transformative education theory and in leadership strategies.
2. To provide Learners key worldview foundations for critical thinking and study.  
3. To provide Learners with practical experience germane to their transformative learning and leadership.  

PLOs for B. Ed: 

1. To prepare Learners for roles in transformative education teaching and service.
2. To provide Learners a foundation for effective individual and organizational leadership in diverse environments.  
3. To ensure Learners demonstrate worldview foundation for empowering people and building communities.  
4. To develop Learners who formulate the Biblical approach to transformative learning and leadership

 

CBU Learning Outcomes (CBULOs)

1. Critical Thinking, Problem Solving, and Research – Learners will demonstrate ability to think critically, solve problems, and conduct interdisciplinary research at a level appropriate to their program.
2. Personal Growth – Learners will understand how learning is related to personal growth, and will be challenged to grow in their thinking, communication, conduct, and engagement with others.
3. Skills Development – Learners will advance in skills related to their area of learning, demonstrating a level of competency appropriate to their program.
4. Social Responsibility – Learners will appreciate the diversity in and value of others as designed by our Creator, and will grow in willingness and capability to serve others.
5. Worldview Applications – Learners will become capable at thinking from a worldview perspective and will understand the relationship of description and prescription, so that they can ground their actions in sound principles.

 

Assignments and Grading (1000 Points)

Module Assessments (50 points each x 10)  

Journals (50 points each x 4)  

Problem Sets (5 points each x 10) 

Course Assessment 

………………Column Break……………… 

500 Points (Multiple Choice + Short Answer) 

200 Points (Essays) 

50 Points (Completion) 

250 Points (Multiple Choice + Short Answer) 

 

Grading Scale

91-100%          A

81-90%            B

71-80%            C

61-70%            D

0-60%              F

 

Carnegie Unit Credit Hour Equivalent

Total Hours of Module Content: 30 hours 

Total Hours of Reading Content: 35 hours 

Total Hours of Practice Problems: 40 hours 

Total Hours of Journal Questions: 15 hours 

Total Hours of Minor Assessments: 10 hours 

Total Hours of Major Assessment: 5 hours 

Equivalent of 3 Credit Hours (135 hours of total course time)