MAE4815

Elements of Algebra

Course Code: MAE4815

Credit Hours: 3

Effective beginning: Fall 2020

 

Course Description:
This course offers an approach to number theory with an emphasis in understanding the nature of integer numbers, congruence classes, and their operations and applications. Topics include divisibility and divisibility tests, greatest common divisor, mathematical induction, division and Euclidian algorithms, primes, congruence, linear Diophantine equations, theorems of Euler and Fermat, linear congruences, and the Chinese Remainder Theorem.

Course Details

Prerequisites:

MAC 1311

Instructors:

Dr. Irma Cruz-White
cruz-whitei@chipola.edu

 

 

Required textbooks/ course materials:

Number Theory: A Lively Introduction with Proofs, Applications, and Stories, Pommersheim, Marks, Flapan, Wiley 2010.  ISBN: 9780470424131

 

Assignment/course outline:

See your Instructor First Day Handout for individual instructor assignment schedule.

 

 

Discipline-level learning outcomes:

MAE 4815 is not a General Education core course.

E – 1  Demonstrate understanding of instructional design and lesson planning by applying concepts from human development and learning theories.

E – 2  Demonstrate ability to maintain a student-centered learning environment that is safe, organized, equitable, flexible, inclusive and collaborative.

E – 3  Demonstrate effective instructional delivery and facilitation by utilizing deep and comprehensive knowledge of core content.

E – 4  Demonstrate understanding of assessment by analyzing and applying data from multiple assessments to diagnose learning needs and inform instruction.

E – 5  Demonstrate continuous improvement by designing purposeful goals to strengthen instructional effectiveness and impact student learning.

E – 6   Demonstrates professional responsibility and ethical conduct and fulfills expected obligations to students, the public, and the education profession.

 

 

Course-level student learning outcomesDiscipline-level learning outcomesAssessment methods

Formulate conjectures, basic proofs and counterexamples involving number theory concepts.

Develop divisibility tests.

Find the greatest common divisor using various methods.

Explore prime numbers.

Solve linear Diophantine equations.

Solve linear and quadratic congruence equations.

Solve systems of congruence equations using the Chinese Remainder Theorem.

Solve problems involving the order of an element in a group.

Explore applications to real-world and mathematical problem-solving situations. 

 

Homework, Report/Presentation, Problem Solving

 

 

Teacher facilitated: The instructor will be leading class discussions on the material during class periods.

Student-centered: The students will practice solving problems and make several presentations during class periods.

Office Hours: The instructor will be available during office hours for individual assistance.

College-wide policies and resources

For more specific information on Chipola's college-wide academic policies and resources available to students, visit the link below.