4. (2 points each) The number of bacteria in a culture doubles every 4 hours. There are 570 bacteria present in the culture initially. (a) Find the growth constant for the culture. (b) How many bacteria will be in the culture after 7 hours? 1 5. (4 points each) Consider the function f (x) = x...

Is a polygonal path joining P and Q such that all of its segments have nonnegative slopes. Show that the taxicab length of Equals dt(P, Q). Is this also true if all of the segments have nonpositive slopes?

Consultation times: Tues 2-3 pm, Wed 11-12am & 4-5pm, 2114& other times by appointment. Appointment. Ch 0 Study Book Appendix A (choice of 2 readings) Ch 1-3 Larson & Edwards 4th or 5th Ed. Why Vectors?

General idea: skim Circle unfamiliar words. Detail: read slowly and reread. Mathematicians hate fluff. What to do?

Which one of the variables is the independent variable (x) and which one is the dependent variable (y)? Why?

2. Suppose A is a permutation matrix. Prove that A-1 = transpose(A). 3. An n N matrix A is called nilpotent if there is a positive integer k such such that Ak is a matrix of zeros. Prove that the determinant of a nilpotent matrix is zero.

Q is epi in the category of rings. (ii) Show that kernels are monic and are unique up to isomorphism. (iii) In Groups, show that monics are injections and kernels are monics with normal image. What are epis and cokernels? 2. (Colimits and van Kampen) (i) What is the coproduct of groups...

1)), i.e. is there a space whose homology is the Rost motive? 2. Is there an algebraic analogue of (4.4) and if yes, what is the algebraic analogue n of 2 (1) KR(n)? 3. Is there a M GL-module decomposition of M GL X for a Pster quadric X analogous to the motivic decomposition constructed by...

If f (x) = e x , then f (n) (x) = e x for all n Find the Maclaurin series for e x . What is its radius of convergence?

1 n x2 x3 x =1+x + + + Find the Maclaurin series for e x . What is its radius of convergence?