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Mathematics 215: Analysis in a Single VariableSyllabusSpring 2013

Instructor:

Mark McConnell (markwm@princeton.edu), Fine Hall 1110Office hours: MWF 11:00-11:50, TTh 12:30-1:20, or by appointment.

Undergraduate Assistants:

Wesley H. Cao (wenyucao@princeton.edu)Office hours: Tue. and Wed., 9:00-10:00 p.m.

Hanxi (Heinrich) H. Jiang (hhjiang@princeton.edu)Office hours: Tuesdays, 2:00-3:00 and 4:30-5:30.

Office locations to be determined.

Overview. This course is an introduction to the algebraic, topological and analytical framework ofmodern mathematics. It begins at the beginning: set theory, real numbers, integers, and the topology ofthe real line. It then covers the calculus of one variable, concentrating on the theoretical aspects thatare skipped in most first-year calculus courses. The emphasis is on learning to understand and toconstruct proofs. The most important prerequisite is a love of the beauty of mathematics, a curiosityabout the inner workings of mathematical ideas, and a willingness to think abstractly.

Book. Apostol, Calculus, vol. I, second edition, John Wiley and Sons, 1967. Despite the name, this isan analysis book, known for its clarity and careful ordering of ideas.

Because of time constraints, not everything in the reading will be discussed in lecture, and noteverything in lecture will be covered in the reading. Students are responsible for both.

Course structure. There will be weekly reading and homework assignments. Homework is due inclass on Thursdays. Late homework will not be accepted, except in cases of serious illness (with adoctor's note) or emergency.

The homework is fairly long and demanding, as in any course where there is a great deal of deepmaterial to cover. Prof. McConnell is always available in office hours to provide assistance inunderstanding the material, as well as advice on how to get started on the problem sets. Theundergraduate assistants will hold regularly scheduled weekly help sections, offering assistance andadvice along the same lines.

Students are welcome to collaborate on the homework. Each student, though, should be building up hisor her own mathematical ability. This individual growth is the basis for the independent work on theexaminations. Make every effort to understand completely the solutions to the problems. The reasonfor grading the problem sets is to ensure that students understand the material and are not makingmistakes of which they are unaware.

There will be a midterm exam during Midterm Week, and a final exam at the end of the semester. Bothof these will be scheduled by the Registrar. Grades will be based 30% on the problem sets, 30% on themidterm exam, and 40% on the final exam.

God ever geometrizes. --Plato (5th cent. B.C.E.)God ever arithmetizes. --C. G. J. Jacobi (1804-1851)

mailto:markwm@princeton.edumailto:wenyucao@princeton.edumailto:hhjiang@princeton.edumailto:wenyucao@princeton.edumailto:hhjiang@princeton.edumailto:markwm@princeton.edu