Pre/co-requisites: Math 6 or Math 138.

Units: 4

Catalog description: Basic structures of modern algebra from a middle school mathematics curriculum perspective. Algebraic structures, polynomial equations, and elementary linear algebra.

Informal course description and goals: The focus of this course is to broaden content knowledge in algebra, aimed at future teachers at the middle school level. Students are expected to gain: (1) comfort, facility and understanding of core algebraic topics and procedures forming the basis of secondary mathematics. (2) a deeper understanding of the key structures of algebra and their interconnections with numeracy and K-12 curricula. (Groups, Rings, Fields and Vector Spaces).

Learning Outcomes
Upon completion of Math 139, students should be able to:

• Have better analytical and logical thinking skills, as well as broader understanding of the role polynomials in mathematics. Emphasis will be placed on the connections between numbers and polynomials through the concept of a ring.
• Be able to communicate algebra related ideas and problems verbally and symbolically as well as construct clear proofs in elementary number theory (proof by mathematical induction).
• Be able to understand and work with key linear algebra concepts such as vectors, matrix arithmetic, row reduction, inverse of a matrix, systems of equations, linear independence/dependence, dot-product, cross-product and determinant.
• Be able to solve various algebra related mathematical problems using the Binomial Expansion concept.
• Be able to define and understand key differences of the four fundamental algebraic structures: (Groups, Rings, Fields and Vector Spaces).

Grading policy: Your grade for the course will be based on your performance on quizzes, homework, and tests.

Tests: There will be three (3) 'collaborative' midterm tests and a MANDATORY 'solo performance' comprehensive 2-hour final exam. Students may use their HOMEWORK PORTFOLIOS (see below) for reference on the final exam, but NOT the collaborative midterms. At the beginning of each midterm, a random partner assigning program will generate random paired teams. In the even of an odd number of students, one group of 3 will be randomly selected (teams are asked to whisper quietly as they discuss their problem solving.) Each student must turn in their own exam and the exams will be graded as if that student took the exam alone (partners may end up with different final scores, based on the quality and correctness of work!). Make-up exams will be given only in cases of a documented serious illness or family emergency. If a student makes up a midterm exam, they will obviously be working non-collaboratively. Calculators are allowed on all exams, but no cell phones are permitted to be out during all exams. No exams are dropped.

Class attendance: It is important to attend every class because group/class discussions are vital for success in the course, especially for the daily quiz and portfolio presentation grades, which are substantial portions of the overall grade.

Daily Quizzes: There will be brief daily quizzes in class on key problem-types that were covered the previous class and assigned as HOMEWORK. Daily quiz problems usually will come from problems in the book similar to assigned problems. The quiz will be given near the end of class and students are required to SHOW WORK. There are no daily quizzes on test days, or on the day after a test was given. Two (2) low daily quiz grades will be dropped. Time will be allotted at the beginning of each class for students to ask about suggested homework problems, with students solving those problems at the board as part of their Daily Homework Presentation grade (see below).

Homework Portfolio: This is a dedicated section of your binder, or a small binder which contains onlyl homework problems. This portfolio is not graded, but its quality will be invaluable for your preparation for the Daily Quizzes, your Homework Check for Understanding (HCfU) presentations and use on the Final Exam.

Homework Check for Understanding Presentations: At the beginning of every non-exam day class, students with homework questions are asked to write which portfolio question # on the board that they need explaining on. On a first-come first serve basis, those wanting to present can put their name next to the question being inquired about, and then present and 'teach' a solution. A student may also put their name on the board for a problem they would like to present on. Only one student may present each problem. The student grade is based on completing 5 presentations (25 pts total) according to the following rubric:

No presentation grades are dropped. Remember, if I have to do the problems, those are lost opportunities for students to fulfill their 5 presentation target. If there are no more opportunities at the end of the course, then a student must potentially take 0's for missing presentations. The purpose of these assignments is to prepare you as a future mathematics teacher and treat the homework problems as if you are an instructor planning to lecture on the problems for a class you are teaching. Again, it is first come first serve for presenting problems.

Computers: At California State University, Fresno, computers and communications links to remote resources are recognized as being integral to the education and research experience. Every student is required to have his/her own computer or have other personal access to a workstation (including a modem and a printer) with all the recommended software. The minimum and recommended standards for the workstations and software, which may vary by academic major, are updated periodically and are available from Information Technology Services or the Universit Bookstore. In the curriculum and class assignments, students are presumed to have 24-hour access to a computer workstation and the necessary communication links to the University's information resources.

Students with disabilities: upon identifying themselves to the University, students with disabilities will receive necessary accommodation for learning and evaluation. For more information, see http://studentaffairs.csufresno.edu/ssd

Academic honesty: cheating and plagiarism will not be tolerated in this class. For information on the University's policy, see the University Catalog (section Policies and Regulations).

Honor Code: Members of the CSU Fresno academic community adhere to principles of academic integrity and mutual respect while engaged in university work and related activities. You should:

• understand or seek clarification about expectations for academic integrity in this course (including no cheating, plagiarism and inappropriate collaboration)
• neither give nor receive unauthorized aid on examinations or other course work that is used by the instructor as the basis of grading.
• take responsibility to monitor academic dishonesty in any form and to report it to the instructor or other appropriate official for action.

Disruptive Classroom Behavior: student conduct which disrupts the learning process will not be tolerated and may lead to disciplinary action and/or removal from class.

Copyright policy: Copyright laws and fair use policies protect the rights of those who have produced the material. The copy in this course has been provided for private study, scholarship, or research. Other uses may require permission from the copyright holder. The user of this work is responsible for adhering to copyright law of the U.S. (Title 17, U.S. Code). To help you familiarize yourself with copyright and fair use policies, the University encourages you to visit its copyright web page: http://www.csufresno.edu/library/libraryinformation/campus/copyright/copyrtpolicyfull.pdf. For copyright Questions & Answers: http://www.csufresno.edu/library/libraryinformation/campus/copyright/faqcopyright.pdf. Digital Campus course web sites contains material protected by copyrights held by the instructor, other individuals or institutions. Such material is used for educational purposes in accord with copyright law and/or with permission given by the owners of the original material. You may download one copy of the materials on any single computer for non-commercial, personal, or educational purposes only, provided that you (1) do not modify it, (2) use it only for the duration of this course, and (3) include both this notice and any copyright notice originally included with the material. Beyond this use, no material from the course web site may be copied, reproduced, re-published, uploaded, posted, transmitted, or distributed in any way without the permission of the original copyright holder. The instructor assumes no responsibility for individuals who improperly use copyrighted material placed on the web site.

Subject to Change: This syllabus and schedule are subject to change in the event of extenuating circumstances. If you are absent from class, it is your responsibility to check on announcements made while you were absent.