MA 225 Foundations
of Advanced Mathematics Spring, 2010

Instructor: Ellen Peterson

Office: SAS 3223

Email: erpeters@ncsu.edu

Office Hours: Monday, Wednesday 1:00-1:30, or by appointment

Classroom: SAS 1218

Time: Tuesday, Thursday 11:45 am-1:00 pm

Prerequisite: Math 241 Elementary Calculus II

Textbook: Smith, Eggen and St. Andre, A Transition to Advanced Mathematics, 6th edition

Course Objectives:

Grading:

1. I encourage you to discuss homework with other students, or with me during office hours. You should be aware that the homework is intended for you to learn from the course; working on homework at least in part on your own will help you master the material, keep up with the course and prepare for tests. Homework will be graded on a scale of 1-10. Points will be awarded for amount of homework attempted; selected problems will be graded in detail.

2. I expect you to read sections of the book around the time of lectures and homework from those sections. The book has additional examples and discussion that you will find helpful. Some test questions may resemble examples from the book.

3. You are expected to attend all classes on time. Classroom discussion and questions in class help clarify issues in this course, so please feel free to participate by asking questions.

4. Arriving late for a class or leaving early is very disruptive of class. If you need to leave early, please let me know at the beginning of class, and sit near the door so you can slip out quietly.

5. If you are unavoidably absent from a test, a score for that test will be assessed at the end of the semester, based on your performance in homework, the other tests, and on the final, with an emphasis on the material of the missed test. View NC State's attendance policy.

Academic Integrity Statement: Students are expected to follow university policies on academic integrity and the Honor Pledge.

Further Statements:

If you are ill with symptoms of H1N1 influenza (i.e. fever over 100, sore throat, cough, stuffy or runny nose, fatigue, headache, body aches, vomiting and diarrhea) please do not come to class. Instead, immediately contact your medical provider or Student Health Services (515-7107) for advice or to arrange an appointment. If you are diagnosed with H1N1, please inform your instructor immediately. You will be required to be isolated away from class until at least 24 hours after you are free of fever (100 degrees), or signs of a fever, without the use of fever-reducing medications.

Reasonable accommodations will be made for students with verifiable disabilities. In order to take advantage of available accommodations, students must register with Disability Services for Students at 1900 Student Health Center, Campus Box 7509, 515-7653. For more information on NC State's policy on working with students with disabilities, please see the Academic Accommodations for Students with Disabilities Regulation (REG02.20.1).

Instructor: Ellen Peterson

Office: SAS 3223

Email: erpeters@ncsu.edu

Office Hours: Monday, Wednesday 1:00-1:30, or by appointment

Classroom: SAS 1218

Time: Tuesday, Thursday 11:45 am-1:00 pm

Prerequisite: Math 241 Elementary Calculus II

Textbook: Smith, Eggen and St. Andre, A Transition to Advanced Mathematics, 6th edition

Syllabus:

Chapter 1: All Sections (3 weeks)

-Propositions, Connectives,
Conditionals, Biconditionals, Quantifiers, Proof Methods

Chapter 2: 2.1-2.4 (2 weeks)

-Set Theory, Set Operations, Families
of Sets, Induction

Chapter 3: 3.1-3.2 (1 week)

-Cartesian Products, Relations,
Equivalence Relations

Chapter 4: 4.1-4.5 (3 weeks)

-Functions, One-to-one, Onto

Chapter 5: 5.1-5.3 (2 weeks)

-Equivalent Sets, Finite Sets,
Infinite Sets, Countable Sets

Course Objectives:

The
primary goal of Math 225 is to prepare you for upper level courses in mathematics, especially courses that
rely on understanding and writing mathematics. The course includes an introduction to the
format of definition, theorem and proof, the design and writing of logical arguments and
formal proofs, and techniques of problem solving in higher level mathematics. During the
semester, fundamental concepts in several areas of mathematics are introduced, partly to
show the structure of mathematical writing in different contexts, but also to lay the
foundations for higher level courses such as abstract algebra and analysis.

Grading:

1. Weekly
Homework Assignments (10% of final grade), due Thursdays (but not always)

2. Three in-class exams (60%)

2. Three in-class exams (60%)

Tentative Dates: Thursday February 11,
Thursday March 11, Thursday April 22

3. Final Exam (30%) Thursday May 6 8:00-11:00 amScale:
90%-100%:A, 80%-89%: B, etc. (+ and - will also be used.)

Additional
Policies:1. I encourage you to discuss homework with other students, or with me during office hours. You should be aware that the homework is intended for you to learn from the course; working on homework at least in part on your own will help you master the material, keep up with the course and prepare for tests. Homework will be graded on a scale of 1-10. Points will be awarded for amount of homework attempted; selected problems will be graded in detail.

2. I expect you to read sections of the book around the time of lectures and homework from those sections. The book has additional examples and discussion that you will find helpful. Some test questions may resemble examples from the book.

3. You are expected to attend all classes on time. Classroom discussion and questions in class help clarify issues in this course, so please feel free to participate by asking questions.

4. Arriving late for a class or leaving early is very disruptive of class. If you need to leave early, please let me know at the beginning of class, and sit near the door so you can slip out quietly.

5. If you are unavoidably absent from a test, a score for that test will be assessed at the end of the semester, based on your performance in homework, the other tests, and on the final, with an emphasis on the material of the missed test. View NC State's attendance policy.

Academic Integrity Statement: Students are expected to follow university policies on academic integrity and the Honor Pledge.

Further Statements:

If you are ill with symptoms of H1N1 influenza (i.e. fever over 100, sore throat, cough, stuffy or runny nose, fatigue, headache, body aches, vomiting and diarrhea) please do not come to class. Instead, immediately contact your medical provider or Student Health Services (515-7107) for advice or to arrange an appointment. If you are diagnosed with H1N1, please inform your instructor immediately. You will be required to be isolated away from class until at least 24 hours after you are free of fever (100 degrees), or signs of a fever, without the use of fever-reducing medications.

Reasonable accommodations will be made for students with verifiable disabilities. In order to take advantage of available accommodations, students must register with Disability Services for Students at 1900 Student Health Center, Campus Box 7509, 515-7653. For more information on NC State's policy on working with students with disabilities, please see the Academic Accommodations for Students with Disabilities Regulation (REG02.20.1).