Semester Project References

2.3 The Field Axioms. (n.d.). Retrieved from http://people.reed.edu/~mayer/math112.html/html1/node16.html/

Algebraic Structrues. (n.d.). Retrieved September 26, 2018, from http://faculty.bard.edu/belk/math332/AlgebraicStructures.pdf/

Basic Properties of Rings. (n.d.). Retrieved September 26, 2018, from http://math.mit.edu/~mckernan/Teaching/12-13/Spring/18.703/l_15.pdf/

Mok, I. A. (2010, June 17). Students' algebra sense via their understanding of the distributive law. Retrieved from https://tandfonline.com/doi/pdf/10.1080/1554480X.2010.486156?needAccess=true/

Ding, M., & Li, X. (2010, April `4). A Comparative Analysis of the Distributive Property in U.S. and Chinese Elementary Mathematics Textbooks. Retrieved from https://tandfonline.com/doi/pdf/10.1080/07370001003638553?needAccess=true/

Teisman, H. (2017, December 13). Toward a More Complete List of Completeness Axioms. Retrieved from https://tandfonline.com/doi/pdf/10.4169/amer.math.monthly.120.02.099?needAccess=true/

Berge, A. (2010, February 15). Students' perceptions of the completeness property of the set of real numbers. Retrieved from https://tandfonline.com/doi/pdf/10.1080/00207390903399638?needAccess=true/

AsKew, A., Kennedy, K., & Kilma, V. (2018, May 9). Modular Arithmetic and Microtonal Music Theory. Retrieved from https://tandfonline.com/doi/pdf/10.1080/10511970.2017.1388314?needAccess=true/

Dobbs, D. E. (2007, July 3). The remainder theorem and factor theorem for polynomials over noncommutative coefficient rings. Retrieved from https://tandfonline.com/doi/pdf/10.1080/00207390600913350?needAccess=true/

Dobbs, D. E. (2016, December 9). The rings with identity whose additive subgroups are one-sided ideals. Retrieved from https://tandfonline.com/doi/pdf/10.1080/0020739X.2016.1264637?needAccess=true/

Historical Overview. (n.d.). Retrieved from http://web.mnstate.edu/peil/geometry/C1AxiomSystem/history.htm/

Algebraic Properties [Axioms]. (n.d.). Retrieved from http://www.doe.virginia.gov/instruction/mathematics/resources/va_algebraic_properties.pdf/

Kiang, L. Y. (n.d.). Axioms and algebraic systems. Retrieved from https://sms.math.nus.edu.sg/smsmedley/Vol-17-1/Axioms and algebraic systems(YK Leong).pdf /

Math 511, Algebraic Systems. (n.d.). Retrieved from https://www.math.ksu.edu/~cochrane/m511/m511axioms.pdf/

Hungerford, T. W. (2014). Abstract Algebra: An introduction (3rd ed.). Boston, MA: Brooks/Cole, Cengage Learning./

Noether, Emmy (1921). "Idealtheorie in Ringbereichen". Math. Annalen. 83: 24-66. doi:10.1007/bf01464225

Abraham Fraenkel (1914) "Uber die Teiler der Null und die Zerlegung von Ringen"

Semester Project Resources

[Khan Academy] (2015, Sept 15) Mathematical Closure. Retrieved from https://www.youtube.com/embed/BXg3cAbmDjM

[Khan Academy] (2010, Aug 2) Associative law of addition | Arithmetic properties | Pre-Algebra | Khan Academy. Retrieved from https://www.youtube.com/watch?v=oTKVXJ7TcbA

[Khan Academy] (2011, Jan 19) Commutative property for addition | Arithmetic properties | Pre-Algebra | Khan Academy. Retrieved from https://www.youtube.com/watch?v=UeG_EYd-0xw

Math Insight. (n.d.). Retrieved from https://mathinsight.org/applet/vector_sum

[TheTrevTutor] (2017, Jun 4) [Mathematical Linguistics] Identity Elements, Inverse Elements, and Zero Elements. Retrieved from https://www.youtube.com/watch?v=QGP19q4zQCk

[Khan Academy] (2017, Oct 19) Associative property of multiplication. Retrieved from https://www.youtube.com/watch?v=Wqxfm7EPcjo

(n.d.). Geometric Proof of the Distributive Property. Retrieved from https://www.geogebra.org/m/jUbGyhdq

[Khan Academy] (2012, Sept 7) How to simplify an expression by combining like terms and the distributive property | Khan Academy. Retrieved from https://www.youtube.com/watch?v=3NHSwiv_pSE

[Khan Academy] (2010, Aug 2) Commutative law of multiplication | Arithmetic properties | Pre-Algebra | Khan Academy. Retrieved from https://www.youtube.com/watch?v=ENKH97PYssg

[Socratica] (2017, Jun 4) Integral Domains (Abstract Algebra). Retrieved from https://www.youtube.com/watch?v=87QXdOxeVmU

[mistercorzi] (2013, Dec 18) 05 The Field of Complex Numbers. Retrieved from https://www.youtube.com/watch?v=QYgnVjUzi10

[Mathoma] (2016, Aug 2) Complex Numbers as Matrices. Retrieved from https://www.youtube.com/watch?v=kst2Io91JbM