Course Description:This course offers an approach to number theory in which students develop their capacity to formulate conjectures and proofs. Topics include divisibility and divisibility tests, greatest common divisor, mathematical induction, division and Euclidian algorithms, primes, number-theoretic functions, congruence, linear Diophantine equations, theorems of Euler and Fermat, linear congruences and the Chinese Remainder Theorem.
Required textbooks/ course materials:
Number Theory: A Lively Introduction with Proofs, Applications, and Stories, Pommersheim, Marks, Flapan, Wiley 2010, ISBN 13: 9780470424131
See first-day handout.
Discipline-level learning outcomes:
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 learning outcomes:
|Course-level student learning outcomes||Discipline-level learning outcomes||Assessment methods|
Formulate conjectures, 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.
Solve applications to real-world and mathematical problem-solving situations.
|Homework, Reports, Problem-Solving, Unit Tests, Final Exams|
Means of accomplishing learning outcomes:
The students will practice solving problems and make several presentations during class periods.
College-wide policies and resources
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