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Abstract Algebra II
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This course is a continuation of Abstract Algebra I: the student will revisit structures like groups, rings, and fields as well as mappings like homomorphisms and isomorphisms. The student will also take a look at ring factorization, general lattices, and vector spaces. Later this course presents more advanced topics, such as Galois theory - one of the most important theories in algebra, but one that requires a thorough understanding of much of the content we will study beforehand. Upon successful completion of this course, students will be able to: Compute the sizes of finite groups when certain properties are known about those groups; Identify and manipulate solvable and nilpotent groups; Determine whether a polynomial ring is divisible or not and divide the polynomial (if it is divisible); Determine the basis of a vector space, change bases, and manipulate linear transformations; Define and use the Fundamental Theorem of Invertible Matrices; Use Galois theory to find general solutions of a polynomial over a field. (Mathematics 232)

Subject:
Algebra
Material Type:
Full Course
Provider:
The Saylor Foundation
Date Added:
03/04/2019
Adult Literacy Fundamentals Mathematics: Book 1
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CC BY
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: Fundamental mathematics for adult learners. Book 1 includes a Table of Contents, Glossary, Grades Records, Self Tests, Practice Tests and Unit Tests. Ancillary Resources include the Instructor's Manual. This is 1 of a series of 6 books in the ABE Math collection.

Subject:
Education
Mathematics
Material Type:
Textbook
Provider:
BCcampus
Provider Set:
BCcampus Open Textbooks
Author:
Liz Gerard
Wendy Tagami
Date Added:
10/28/2014
Adult Literacy Fundamentals Mathematics: Book 2
Unrestricted Use
CC BY
Rating

: Fundamental mathematics for adult learners. Book 2 includes a Table of Contents, Glossary, Grades Records, Self Tests, Practice Tests and Unit Tests. Ancillary Resources include the Instructor's Manual. This is 1 of a series of 6 books in the ABE Math collection.

Subject:
Education
Mathematics
Material Type:
Textbook
Provider:
BCcampus
Provider Set:
BCcampus Open Textbooks
Author:
Liz Gerard
Wendy Tagami
Date Added:
10/28/2014
Adult Literacy Fundamentals Mathematics: Book 3
Unrestricted Use
CC BY
Rating

: Fundamental mathematics for adult learners. Book 3 includes a Table of Contents, Glossary, Grades Records, Self Tests, Practice Tests and Unit Tests. Ancillary Resources include the Instructor's Manual. This is 1 of a series of 6 books in the ABE Math collection.

Subject:
Education
Mathematics
Material Type:
Textbook
Provider:
BCcampus
Provider Set:
BCcampus Open Textbooks
Author:
Liz Gerard
Wendy Tagami
Date Added:
10/28/2014
Adult Literacy Fundamentals Mathematics: Book 4
Unrestricted Use
CC BY
Rating

: Fundamental mathematics for adult learners. Book 4 includes a Table of Contents, Glossary, Grades Records, Self Tests, Practice Tests and Unit Tests. Ancillary Resources include the Instructor's Manual. This is 1 of a series of 6 books in the ABE Math collection.

Subject:
Education
Mathematics
Material Type:
Textbook
Provider:
BCcampus
Provider Set:
BCcampus Open Textbooks
Author:
Liz Gerard
Wendy Tagami
Date Added:
10/28/2014
Adult Literacy Fundamentals Mathematics: Book 5
Unrestricted Use
CC BY
Rating

: Fundamental mathematics for adult learners. Book 5 includes a Table of Contents, Glossary, Grades Records, Self Tests, Practice Tests and Unit Tests. Ancillary Resources include the Instructor's Manual. This is 1 of a series of 6 books in the ABE Math collection.

Subject:
Education
Mathematics
Material Type:
Textbook
Provider:
BCcampus
Provider Set:
BCcampus Open Textbooks
Author:
Liz Gerard
Wendy Tagami
Date Added:
10/28/2014
Adult Literacy Fundamentals Mathematics: Book 6
Unrestricted Use
CC BY
Rating

: Fundamental mathematics for adult learners. Book 6 includes a Table of Contents, Glossary, Grades Records, Self Tests, Practice Tests and Unit Tests. Ancillary Resources include the Instructor's Manual. This is 1 of a series of 6 books in the ABE Math collection.

Subject:
Education
Mathematics
Material Type:
Textbook
Provider:
BCcampus
Provider Set:
BCcampus Open Textbooks
Author:
Liz Gerard
Wendy Tagami
Date Added:
10/28/2014
Advanced Partial Differential Equations with Applications, Fall 2009
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CC BY-NC-SA
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" The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate various scientific disciplines. The emphasis is on nonlinear PDE. Applications include problems from fluid dynamics, electrical and mechanical engineering, materials science, quantum mechanics, etc."

Subject:
Algebra
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Rosales, Rodolfo R.
Date Added:
01/01/2009
Advanced Statistics
Unrestricted Use
CC BY
Rating

This course is oriented toward US high school students. The course is divided into 10 units of study. The first five units build the foundation of concepts, vocabulary, knowledge, and skills for success in the remainder of the course. In the final five units, we will take the plunge into the domain of inferential statistics, where we make statistical decisions based on the data that we have collected.

Subject:
Statistics and Probability
Material Type:
Full Course
Provider:
The Saylor Foundation
Date Added:
03/04/2019
Air Pollution [Liberal Arts: Math and Science/Natural Science]
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CC BY
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This assignment was designed for students in the pathways introductory chemistry class and the first year seminar and aligns with the Inquiry and Problem Solving core competency. In this context, there is a focus on framing the issues (identifies and/or addresses questions and problems), evidence gathering (assembles, reviews and synthesizes evidence from several diverse sources), evidence (analyze the data to address the questions posed) and conclusions (critical thinking, reflect on the outcomes, draw conclusions and generate new knowledge). There is also a Global Learning component based on comparing data collected locally with corresponding data from other locations or countries. The assignment includes the written communication ability with a focus on "Content Development and Organization," as well as the clarity of the communication and its purpose. The overall aim of this assignment is to enhance students' conceptual learning and understanding of key issues related to society as well as their course. This assignment was developed as part of a LaGuardia Global Learning mini-grant and CUNY Experiential Learning and Research in the Classroom mini-grants.
The assignment will be scaffolded over about 3 weeks and is worth about 10% of the final grade.
To further increase the success of this assignment, instructors might want to consider the following: Use class discussions to focus on the relevance and importance of conceptual learning. In order to improve the data analysis aspect, incorporating class demonstrations of how to conduct the analysis and guide discussions about what the data means. Giving students more detailed rubrics with formal expectations of the requirements of the assignments, particularly in the written format Find ways to increase student participation in class discussions.
When this assignment has been utilized in previous semesters, students clearly displayed the capability to relate the co-curricular experiences in the data collection and its analysis to concepts and ideas covered during class. Evidence for this came from very dynamic and interactive class discussions based on air pollution as well as from the output of the written assignment, in which students were able to relate the nature, sources and chemical properties of the pollutants to their impact on the environment, health and society in general.
LaGuardia's Core Competencies and Communication Abilities
List the Program Goal(s) that this assignment targets
Global Learning based on comparing pollutant levels around the LaGuardia campus with those in other locations or countries. It is also an IPS assignment, incorporating scientific literacy and thinking, as students need to analyze the data, interpret it and reflect on the outcomes.
List the Student Learning Objective(s) that this assignment targets
Identify and apply fundamental chemical concepts and methods. Gather, analyze, and interpret data.
List the Course Objectives(s) that this assignment targets
Explore the complex connections between chemistry and society. Apply chemical principles to real world issues, including ethical aspects. Gather, analyze, and interpret data.
Write a short description of the pedagogy involved in executing this assignment
Students collect and analyze the data, interpret the results in terms of pollution levels, safety and ethics and compare with EPA standard levels and with levels in other countries.
Outside the classroom events will be organized for data collection. There will be class and group-based discussions focused on the data, its analysis and the connections to society.

Subject:
Environmental Science
Biology
Statistics and Probability
Chemistry
Physical Geography
Material Type:
Homework/Assignment
Provider:
CUNY Academic Works
Provider Set:
LaGuardia Community College
Author:
Alberts, Ian
Date Added:
10/01/2018
Algebra
Unrestricted Use
CC BY
Rating

This course discusses how to use algebra for a variety of everyday tasks, such as calculate change without specifying how much money is to be spent on a purchase, analyzing relationships by graphing, and describing real-world situations in business, accounting, and science.

Subject:
Algebra
Material Type:
Full Course
Provider:
The Saylor Foundation
Date Added:
03/04/2019
Algebra2Go - Prealgebra
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Prepare yourself to take an Algebra course with the Algebra2go䋢 prealgebra resources page. Whether you are attending Saddleback College's prealgebra class (math 351), taking a prealgebra class at another school, or need to refresh your math skills for a business or science class, Professor Perez and his favorite student Charlie have the tools that can help you. We have five primary types of study materials: class notes, video worksheets, video lectures, practice problems, and practice quizzes. For some topics we have some additional tools to assist you.

Subject:
Algebra
Material Type:
Full Course
Homework/Assignment
Lecture
Lecture Notes
Provider:
Saddleback College
Provider Set:
Individual Authors
Author:
Candice Harrington
Larry Perez
Patrick Quigley
Date Added:
03/04/2019
Algebra2go:  Decimals
Conditional Remix & Share Permitted
CC BY-SA
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Part of the course for community college students featuring Professor Perez and his student Charlie, teaching about decimal concepts and operations.

Subject:
Algebra
Material Type:
Activity/Lab
Full Course
Homework/Assignment
Lecture
Provider:
Saddleback College
Provider Set:
Individual Authors
Author:
Candice Harrington
Larry Perez
Patrick Quigley
Date Added:
03/04/2019
Algebra2go- PreAlgebra - Intro to Subtraction
Conditional Remix & Share Permitted
CC BY-SA
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This course is for community college students featuring Professor Perez and his student Charlie. This lesson demonstrates subtraction, including when the answer is negative, on the number line.

Subject:
Algebra
Material Type:
Assessment
Full Course
Lecture
Lecture Notes
Provider:
Saddleback College
Provider Set:
Individual Authors
Author:
Candice Harrington
Larry Perez
Patrick Quigley
Date Added:
03/04/2019
Algebra2go: Pre-algebra Conversions
Unrestricted Use
CC BY
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This is part of the course for community college students featuring Professor Perez and his student Charlie, teaching how to make conversions between different kinds of units.

Subject:
Algebra
Material Type:
Activity/Lab
Full Course
Lecture
Unit of Study
Provider:
Saddleback College
Provider Set:
Individual Authors
Author:
Candice Harrington
Larry Perez
Patrick Quigley
Date Added:
03/04/2019
Algebra II, Spring 2011
Conditional Remix & Share Permitted
CC BY-NC-SA
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This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory.

Subject:
Algebra
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Artin, Michael
Date Added:
01/01/2011
Algebra and Trigonometry
Unrestricted Use
CC BY
Rating

Algebra and Trigonometry provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensures that the book meets the needs of a variety of courses. Algebra and Trigonometry offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.

Subject:
Algebra
Trigonometry
Material Type:
Textbook
Provider:
Rice University
Provider Set:
OpenStax College
Author:
David Lippman
Jay Abramson
Jean-Marie Magnier
Melonie Rasmussen
Nicholas Belloit
Rachael Gross
Rick Norwood
Valeree Falduto
Date Added:
01/29/2015
Algebraic Geometry, Spring 2009
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

" This course provides an introduction to the language of schemes, properties of morphisms, and sheaf cohomology. Together with 18.725 Algebraic Geometry, students gain an understanding of the basic notions and techniques of modern algebraic geometry."

Subject:
Algebra
Geometry
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Kedlaya, Kiran
Date Added:
01/01/2009
Analysis I, Fall 2010
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CC BY-NC-SA
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Analysis I covers fundamentals of mathematical analysis: metric spaces, convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations.

Subject:
Mathematics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Wehrheim, Katrin
Date Added:
01/01/2010