MATH2101 College Algebra
COURSE PREVIEW AND SYLLABUS
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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.
Jeffrey R. Christianson, Ph.D
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
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.
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]
Course Learning Outcomes (CLOs)
- Demonstrate an intuitive understanding of the language of algebra (CBULO 1, 2, BPCO 1).
- Apply this understanding to define and solve practical problems (CBULO 2, 3, BPCO 2, APCO 1).
- 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)
- 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.
- 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.
- Skills Development – Learners will advance in skills related to their area of learning, demonstrating a level of competency appropriate to their program.
- 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.
- 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)
500 Points (Multiple Choice + Short Answer)
200 Points (Essays)
50 Points (Completion)
250 Points (Multiple Choice + Short Answer)
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)
Course Duration Policy
Learners may complete the course in as few as four weeks and in as many as sixteen weeks from the date of enrollment.
Writing Style Policy
All written assessments must follow the style guide appropriate for each course subject as listed below:
- PHIL/HUMA/HIST/LANG/BIBL – Chicago Style (The Chicago Manual of Style: The Essential Guide for Writers, Editors, and Publishers, Seventeenth Edition)
- EDUC/SCIE/MATH/PSYC – APA Style (The Publication Manual of the American Psychological Association, Seventh Edition)
- ENGL – MLA Style (MLA Handbook, Ninth Edition)
Standard of Intellectual Honesty
By enrolling in a CBU degree program, Learners commit that they will not give or receive aid in any work that is to be used by the professor as the basis of grading, and that, and will do their part to ensure that other Learners uphold CBU's Standards of Intellectual Honesty.
The CBU faculty manifests its confidence in the honor of its Learners by refraining from proctoring examinations and from taking unusual and unreasonable precautions to prevent intellectual dishonesty.
While the CBU faculty alone has the right and obligation to determine academic requirements, Learners and faculty collaborate to establish the conditions for learning that is worthy of the worldview that CBU represents.
Intellectual dishonesty includes but is not limited to:
- Copying from another’s work or allowing another to copy from one’s own work
- Representing as one’s own work the work of another
- Other forms of plagiarism.
- Unpermitted collaboration or provision of aid on an academic assignment
- Using the same paper or other coursework too satisfy the requirements of more than one course or degree
The standard penalty for a first offense may include a failing grade for the course in which the violation occurred. Repeated offenses may include academic suspension or dismissal.