Classroom sociomathematical norms for proof presentation in undergraduate in abstract algebra

2012 ◽  
Vol 31 (3) ◽  
pp. 401-416 ◽  
Author(s):  
Timothy Fukawa-Connelly
Keyword(s):  
Abstract Algebra ◽  
Sociomathematical Norms ◽  
Proof Presentation

scholarly journals Including School Mathematics Teaching Applications in an Undergraduate Abstract Algebra Course

PRIMUS ◽  
2021 ◽  
pp. 1-29
Author(s):  
James A. Mendoza Alvarez ◽  
Andrew Kercher ◽  
Kyle Turner ◽  
Elizabeth G. Arnold ◽  
Elizabeth A. Burroughs ◽  
...  
Keyword(s):  
Mathematics Teaching ◽  
Abstract Algebra ◽  
School Mathematics

scholarly journals Mathematics in the Digital Age: The Case of Simulation-Based Proofs

2021 ◽  
Author(s):  
Moritz Lucius Sümmermann ◽  
Daniel Sommerhoff ◽  
Benjamin Rott
Keyword(s):  
Dynamic Geometry ◽  
User Interaction ◽  
Alternative Form ◽  
Sociomathematical Norms ◽  
Mathematical Proofs ◽  
Mathematical Simulations ◽  
Simulation Based ◽  
Actual Use ◽  
Theory Yield ◽  
Functions Of Proof

AbstractDigital transformation has made possible the implementation of environments in which mathematics can be experienced in interplay with the computer. Examples are dynamic geometry environments or interactive computational environments, for example GeoGebra or Jupyter Notebook, respectively. We argue that a new possibility to construct and experience proofs arises alongside this development, as it enables the construction of environments capable of not only showing predefined animations, but actually allowing user interaction with mathematical objects and in this way supporting the construction of proofs. We precisely define such environments and call them “mathematical simulations.” Following a theoretical dissection of possible user interaction with these mathematical simulations, we categorize them in relation to other environments supporting the construction of mathematical proofs along the dimensions of “interactivity” and “formality.” Furthermore, we give an analysis of the functions of proofs that can be satisfied by simulation-based proofs. Finally, we provide examples of simulation-based proofs in Ariadne, a mathematical simulation for topology. The results of the analysis show that simulation-based proofs can in theory yield most functions of traditional symbolic proofs, showing promise for the consideration of simulation-based proofs as an alternative form of proof, as well as their use in this regard in education as well as in research. While a theoretical analysis can provide arguments for the possible functions of proof, they can fulfil their actual use and, in particular, their acceptance is of course subject to the sociomathematical norms of the respective communities and will be decided in the future.

A Little Color in Abstract Algebra

1982 ◽  
Vol 89 (6) ◽  
pp. 417 ◽  
Author(s):  
G. P. Wene
Keyword(s):  
Abstract Algebra

scholarly journals Dreibens Modulo 7: A New Formula for Primality Testing

Elements ◽  
2016 ◽  
Vol 12 (1) ◽  
Author(s):  
Arthur Diep-Nguyen
Keyword(s):  
Number Theory ◽  
Linear Algebra ◽  
Abstract Algebra ◽  
Additional Insight ◽  
Primality Testing ◽  
New Formula ◽  
Insight Into ◽  
Rule Out

In this paper, we discuss strings of 3’s and 7’s, hereby dubbed “dreibens.” As a first step towards determining whether the set of prime dreibens is infinite, we examine the properties of dreibens when divided by 7. by determining the divisibility of a dreiben by 7, we can rule out some composite dreibens in the search for prime dreibens. We are concerned with the number of dreibens of length n that leave a remainder i when divided by 7. By using number theory, linear algebra, and abstract algebra, we arrive at a formula that tells us how many dreibens of length n are divisible by 7. We also find a way to determine the number of dreibens of length n that leave a remainder i when divided by 7. Further investigation from a combinatorial perspective provides additional insight into the properties of dreibens when divided by 7. Overall, this paper helps characterize dreibens, opens up more paths of inquiry into the nature of dreibens, and rules out some composite dreibens from a prime dreiben search.

CARRY GROUPS: ABSTRACT ALGEBRA PROJECTS

PRIMUS ◽  
2004 ◽  
Vol 14 (3) ◽  
pp. 258-268
Author(s):  
Cheryl Chute Miller ◽  
Blair F. Madore
Keyword(s):  
Abstract Algebra

scholarly journals Validity of The Abtract Algebra Teaching Book

2020 ◽  
Vol 4 (1) ◽  
pp. 17-23
Author(s):  
Leo Adhar Effendi ◽  
Sindi Amelia
Keyword(s):  
Small Groups ◽  
Formative Evaluation ◽  
Field Tests ◽  
Abstract Algebra ◽  
Development Research ◽  
Evaluation Design ◽  
Self Evaluation ◽  
High Level ◽  
Very High ◽  
Difficult Subjects

The Abstract Algebra is one of the most difficult subjects for students. In this course, students are required to have several textbooks as their reading source. However, the existing textbooks do not guide students in carrying out the process of preparing evidence and tend to speak non-Indonesian languages. The purpose of this research is to design and develop textbooks on abstract algebra courses which contain proofs in full step by step that can improve the ability to organize evidence. This type of research is development research with formative evaluation design consisting of self-evaluation, prototyping (expert reviews, one-to-one, and small groups), and field tests. The validity of the development of abstract algebra textbook is passed through the stages of self-evaluation and expert reviews. The results showed that the prototype of abstract algebra teaching books had a very high level of validity (89.29%).

Sign in / Sign up

Export Citation Format

Share Document