The goal of this course is to study the real numbers. We will, in particular, study the underlying theoretical foundations of calculus. The material is of basic importance not only to (essentially) all of mathematics, but also to the physical sciences and engineering. We should meet a lot of really cool ideas along the way. So while I expect the course to be challenging (to us all), I also hope that it is equally rewarding.CONTENT:
The official course description includes the following: The real number system. Sequences, limits, and continuous functions in R and 'Rn'. The concept of a metric space. Uniform convergence, interchange of limit operations. Infinite series. Mean value theorem and applications. The Riemann integral.COURSEWORK:
The work done in conjunction for this course will consist of weekly homework assignments, one in-class midterms, and one final exam. The weekly homework assignments will be posted at http://math.berkeley.edu/~dkarp/courses/2008Spring/104/homework/GRADES:
Grades may be determined as follows:
The required text for this course is Elementary Analysis: The Theory of Calculus, By Kenneth A. Ross.POLICY:
Late homework may have points deducted. Make-up exams are not allowed unless there is notification 24 hours in advance and is authorized by me, or in case of extreme emergency with written verification.