MATH 231—Geoemtery I

Spring 2010

 

SYLLABUS

MISSION STATEMENT

Felician College is an independent co-educational Catholic/Franciscan College founded and sponsored by the Felician Sisters to educate a diverse population of students within the framework of a liberal arts tradition.  Its mission is to provide a full complement of learning experiences, reinforced with strong academic and student development programs designed to bring students to their highest potential and prepare them to meet the challenges of the new century with informed minds and understanding hearts.  The enduring purpose of Felician College is to promote a love for learning, a desire for God, self knowledge, service to others, and respect for all creation.

 

DIVISION OF ARTS AND SCIENCES MISSION STATEMENT

The mission of the Division of Arts and Sciences is to implement and manifest the Mission of Felician College in the Programs of the Division; the General Education Program, the Developmental Educational Program, and the Core by providing the highest quality of instruction at both the undergraduate and graduate level, encouraging students to develop to their fullest potential, to gain skills for life-long learning, and to produce graduates well-equipped to contribute to society. The division achieves the stated mission by using processes of continual improvement, based upon assessment of student learning at al levels, as well as the assessment of the administrative processes and mechanisms

 

DEPARTMENT OF MATHEMATICAL SCIENCES MISSION STATEMENT

The Department of Mathematical Sciences supports the mission of Felician College by providing the portion of students’ educational experiences dealing with quantitative literacy.  The Department supports the mission of Felician College to provide a strong academic program by providing rigorous mathematics courses to students in all majors at all levels.  The Department supports the mission of the Division of Arts and Sciences by providing a high quality of instruction in mathematics at both the college level and the developmental level.  The broad variety of courses offered by the Department of Mathematical Sciences helps bring students to their highest potential by providing theory and practice related to problem solving, logical reasoning, and analytical skills.  This will help prepare Felician College students to meet future challenges with informed mathematical minds.

 

DISCLAIMER

This syllabus is subject to change according to the needs of the class as deemed appropriate by the instructor.  In case of changes, students will be notified in class and a new syllabus will be distributed.

 

 

Division	Arts and Sciences
Department:	Mathematical Sciences
Course Number	MATH 365R
Course level:	Undergradute
Course Title:	Differential Equations
Instructor:	Dr. Michael Sanford, Ph.D.
Rank:	Associate Professor
Email:	sanfordm@felician.edu or msanfordphd@optonline.net
Phone:	201 559- 6000 ext. 3192
Office	Office: Room 3 Martin Hall Rutherford Campus, (or the Math Lab MH 4)
Division	Arts and Sciences
Department:	Mathematical Sciences
Course Number	MATH 365
Course Title:	Differential Equations
Instructor:	Dr. Michael Sanford
Email:	sanfordm@felician.edu or msanfordphd@optonline.net
Phone:	201 559- 6000 ext. 3192
Office	Office: Room 3 Martin Hall Rutherford Campus, (or the Math Lab MH 4)

 

Course Description:

This course deals with the historical evolution of geometric concepts and Euclidean geometries. This course will also introduce an axiomatic system; students will learn to read and write proofs using this system of axioms and postulates. Topics include inductive and deductive reasoning, symmetry, tessellations, congruence, similarity, and coordinate and transformational geometry. Prerequisite: MATH 114 or MATH 160 or equivalent.

 

Course Objectives:

·       Students will write proofs that involve theorems from algebra, whereby they demonstrate their knowledge of all real number properties.

·       Students will understand the Van Hiele Levels of learning.

·       Students will have a minimal understanding of the historical background of  geometry and its implication to other areas of mathematics and other topics.

·       The student will be able to show an understand of  informal logical deduction by being able to construct geometric figures using the traditional tools of compass and straight edge and list the steps that they followed during the construction.

·       The student will be able to show an understand of formal   deduction by being able to read & write geometric proofs in both statement-reason style and paragraph style.

·       Students will be able to symbolically represent “real life” objects as standard Euclidean geometric figures.

 

 

Text Requirements: Geometry Notes, M. Sanford (No Cost if bring you own storage device otherwise you’ll need to reimburse Dr. Sanford.)

 

Course Content:

Grading Policies

1. Daily Homework: 20% of the total grade. Homework will consist of two pieces 1.) Students will be expected to proofs and problems as assigned and 2.) Students will be expected to put proofs on the board at the beginning of every class period. Since there are more students than problems it should understood and adhered to that you will take turns putting your problems on the board.
2. Exams: 15% each of the total grade. There will three in class exams during the semester. (for a total of 45% of the grade)
3. Final Exam: 35% of the total grade. The final will be a comprehensive exam, date when the registrar’s office informs us.

 

 

 

 

 

 

 

 

 

GRADING RUBRIC:

For any non-proof or construction problems that may arise. The student gets full credit for a quiz or exam question only if the answer is correct, all work is shown, and the work shown leads to the correct answer. Partial credit is given under the following circumstances:

• If the work is substantially correct but there is a minor error in arithmetic, the student will get close to full credit.

·       If there are some mistakes but the student has shown an understanding of at least some of the math, the student will get credit proportional to the amount of understanding demonstrated.

 

Proof Writing

Point Value	Logic and Reasoning	Computation	Communication
4	-Arguments are correct with logical order. −Solution strategy appropriate and comparable to that used by an experienced proof writer −May suggest alternative approaches	−Computations are completed accurately and efficiently −May suggest alternative approaches	−Problem, hypothesis, and conclusion clearly stated −Proof is written in complete sentences with no errors in grammar or spelling −No extraneous information included
3	−Arguments are correct, but awkward in order −Solution strategy appropriate	−Computations are completed accurately	−Problem, hypothesis, and conclusion stated −Proof is written with minor errors in grammar or spelling −Some extraneous information present
2	−Some flaws in arguments −Solution strategy appropriate, but not implemented correctly	−Some minor flaws in computations	−Problem, hypothesis, or conclusion not stated −Proof is written without complete sentences or other errors in grammar or spelling
1	−Arguments are incorrect −Solution strategy inappropriate or not apparent	−Flawed Computations	−Problem not stated −Hypothesis and conclusion not stated −Proof is written without complete sentences and other errors in grammar and spelling are present
0	−Work is nonexistent or unrelated	−Work is nonexistent or unrelated	−Work is non-existent or unrelated

 

GEOMETRIC CONSTRUCTIONS:

 

Points earned	Constructions	Description.
4	Construction completed with compass and straight edge showing appropriately drawn and labeled, intersections, lines, line segments, polygons, circles and arcs.	-Descriptions are correct with logical order. −Construction strategy can be followed and repeated.
3	Construction completed with compass and straight edge showing appropriately drawn and labeled, intersections, lines, line segments, polygons, circles and arcs with two or less *minor errors.	-Description are correct, but awkward in order − Construction strategy appropriate can be generally followed and repeated.
2	Construction not completed or the construction completed with compass and straight edge with more than two *minor errors or one !major error.	- Some flaws in arguments − Construction strategy appropriate, but not implemented correctly
1	Construction is not recognizable or construction completed with two or more!major errors.	- Description are not correct, − Construction strategy cannot be generally followed or repeated.
0	No construction completed or construction completed without the use of a compass and/or straight edge.	Work is non-existent or unrelated

 

Minor Error:

Obvious free-hand extensions or arcs or lines

Lines and/or arcs do not pass through appropriate intersections

Use of inappropriate intersection

Compass or straight edge slippage

 

 Major Error:

Construction is done free hand (drawn without the use of a compass and/or straightedge).

Construction lines or arcs erased

Inappropriate compass setting

 

Geometric constructions are performed using only points, lines, line segments and circles. In many constructions you will use only part of the circle (arc). You cannot use the graduation on your ruler; you are to assume that the centimeter and the inch do not exist. A point is formed only by the intersection of two lines, two arcs, or a line and an arc. Do not draw points so that they have width, a point only has a location. All geometric constructions should be done in pencil on blank white paper.

 

BOARD WORK;

The student will put a proof, construction, or problem on the board at the beginning of each class. The student will be expected to pick a problem that is particularly difficult so that it can be critiqued by class members and or the instructor. Failure to participate will result in a deduction of points commensurate to the number of times the student fails to participate. There is no right or wrong, in fact problems that are incorrect will be preferable to correct ones. This grade is solely a participation grade. If Dr. Sanford needs to ask it will be understood as an automatic deduction from the homework, therefore it is expected that problems will be on the board at the beginning of class without being asked to do so. 

 

 

ASSIGNED PROOF CRITIQUING:

 

On occasion Dr. Sanford will pick someone from the class to critique a proof. The purpose of this is to assess the student’s ability to read critically. 

 

Point value	Logic and Reasoning	Format
4	-Recognizes all errors in logic, order of arguments, calculations, and solution strategy −Provides suggestions to the writer toward solving all problems with arguments, strategy, and calculations	−Recognizes all structural errors in statement of problem and proof −Identifies all extraneous information −Finds all errors in grammar and spelling
3	-Recognizes major errors in logic, calculations, and solution strategy −Provides suggestions to the writer toward solving major problems recognized −Recognizes awkwardness of poorly ordered arguments, but unable to suggest appropriate solutions	−Recognizes most structural errors in statement of problem and proof −Finds most errors in grammar and spelling
2	−Recognizes some major errors in logic, calculations, and solution strategies −Fails to find flaws in poorly ordered arguments −Unable to provide suggestions to the writer toward solving the problems recognized	−Fails to recognize major structural errors instatement of problem and proof −Unable to find most errors in grammar and spelling
1	−Fails to recognize any problem with an incorrect proof or wrongly cites an accurate statement or strategy as inaccurate −Provides no hints, even if a problem is noted	−Fails to recognize any structural problems in a poorly presented proof −Unable to recognize any errors in grammar and spelling
0	−Critique is non-existent or unrelated to task or complete refusal to participate.	−Critique is non-existent or unrelated to task or complete refusal to participate.

 

 

 

Course Policies:

 

Late Homework will be accepted at a reduction of commensurate to the time late.

 

Missed exams, will not be made up unless there is an extreme need. Otherwise you final will become a 300 point final if you need to miss. If you do not talk with me about missing the exam in person I will assume you skipped and expect a 0.

 

In class behavior, I expect you to act as the adult you are and respect your classmates and myself which means the golden rule applies.

 

Academic dishonesty, you are expected to work on your own unless otherwise directed. Quizzes will occasionally be a group effort.

 

 

Note: College Wide Policies can be found in the College Catalog.