Math 411-Autumn 2011
Final Exam and Course Grade Stats
Here is the key information. Grades have been submitted to the
registrar. You can pick up your final exam anytime winter quarter
2012. After one year, I have unclaimed exams destroyed. Have a relaxing
break. I look forward to exposing some of you to more abstract algebra during
winter quarter. I hope Adam's decompression event on the Ave was well
attended and successful.
Here is the distribution of final exam scores:
Here is the distribution of course percentages based on the syllabus
formulas of 30% homework, 30% midterm and 40% final. I dropped 5% of the
homework points:
Here is the distribution of course grades:
Handouts
Here are selected materials related to my Math 411 class during
Autumn 2011.
HOMEWORK and EXAMS
All homework is due at 9:30am the indicated day. No late homework
accepted.
- Homework 1: Due Sept 30, 9:30am.
- Homework 2: Due October 10, 9:30am.
- Sec 1.2: 1-11.
- Sec 1.3: 1,3,6,7-11,13.
- Sec 1.1: 1(i)
- Suppose you can only buy McNuggets in boxes of sizes 4 and 11.
Show there a largest total
number of McNuggets you cannot buy; i.e. there is a largest
(4,11)-inaccessible integer. Justify your
answer following the approach used in homework 1.
- Grading: 10pts each for 1.2(6,7,10) and 1.3(6,10) and inaccessible
problem, for total of 60 pts. 4 pts each for remaining 16
problems. Total possible was 124 pts.
- Solutions.
- Stats: Possible=124; Median=115; Max=124; Min=60.
- Homework 3: Due Oct. 17, 9:30am.
- Homework
#3.
- Grading: 10pts each for problems 1,3,4; 20 pts for problem 8; 10pts
each for 1.4(2,8) and 1.7(2,6,12). 5 pts for trying on all others. Total
possible was 135 pts.
- Solutions.
- Stats: Possible=135; Median=97; Max=131; Min=19.
- Homework 4: Due Oct. 24, 9:30am.
- Homework
#4.
- Grading: 15pts for problem 1, 10 points for problem 2. In problem
3, 10 points each for (6,8,12,14). In problem 3, 10 points each for
(6,7,8,10,14). For remaining problems in 2.1 and 2.4, 5 points each for
effort. Total possible is 195 points.
- Solutions.
- Stats: Possible=195; Median=167; Max=193; Min=72.
- MIDTERM: Friday Oct. 28, 9:30am
- Midterm.
- Solutions.
- Here is the midterm score distribution out of 75:
- Calculate percentage so far:
50*(total homework points on homeworks
1,2,3)/269 + 50*(midterm score)/75. Here is the distribution:
- Calculate grade estimate based on this formula:
0.0545455*(percentage) -0.909091. This is coming from a linear scale
where 90%=4.0 and 68%=2.8. Here is the distribution of estimated
grades so far:
- Calculate grade estimate based on this formula:
- Homework 5: Due Nov. 9, 9:30am.
- Sec. 2.5: All problems
- Sec. 2.6: All problems
- Problem 5 from midterm.
- Grading: From section 2.5: 4,8,14,16 for 15 points each;. 4pts each
for the other 14 problems
for effort if you did anything.
So 60+56=116 points on this section. In
section 2.6: carefully grade 4,12,16 for 15 points each. 4pts each for
the other 13 problems if
you did anything. So 45+42=87 points on this. Gives a grand total of 203
points on this homework.
- Solutions.
- Solutions
Corrections.
- Stats: Possible=221, Median=181; Max=213; Min=80.
- Homework 6: Due Nov. 18, 9:30am.
- Sec. 3.1: 1-7, 9-14, 16.
- Sec. 3.2: 1,3-8.
- Factor these polynomials into irreducible polynomials in R[x],
where R=real numbers: f(x)=x^5 - 1 and f(x)=x^6 - 1. Make sure to justify
your answers.
- Factor these polynomials into irreducible polynomials in C[x],
where C=complex numbers: f(x)=x^5 - 1 and f(x)=x^6 - 1. Make sure to justify
your answers.
- Grading: section 3.1: carefully grade 2,4,10,12,16 for 10 points
each.
5 pts for each of the remaining 9 problems
if they did it.
total of 50+45=95 on this.
section 3.2: carefully grade 4i,6,8 10 points each. 5 pts each for each of the reminain 4 problems
if they did it. total of 40+20=60 pts on this part.
carefully grade problem about factoring x^5-1 and x^6-1 over R for 20 points. 10pts if
they did the last question of factoring these over C. total 30 pts on this part.
grand total: 175pts
- Solutions.
- Stats: Possible=175; Median=140; Max=172: Min=75.
- Homework 7: Due Dec. 2, 9:30am.
- Sec.3.4:2,4,5,7.
- Prove: Suppose f(x) and g(x) are primitive polynomials in Z[x] and
n and m are integers. If nf(x)=mg(x), then n=m and f=g.
- page 184-5: 10,12,14.
- Sec.3.5:2,6,7.
- Determine if these polynomials are irreducible in Q[x]: f=x^22 +
7x^3 +7, g=6x^31+35x^21 + 245 x^11 +175.
- Is x^5 + x^2 +1 irreducible in Q[x]? Justify.
- Is x^5 +x^4 +2x^3 +2x +2 irreducible in Q[x]? Justify.
- Write down all irreducible second and third degree polynomials
in Z_2[x].
- Consider the cubic polynomial f(x)=x^3-2x +4.
- Using the techniques
in section 3.6, calculate the three roots in the form given at the top
of page 148.
- Then simplify them as much as
possible.
(Hint: calculate (-1+sqrt(3)/3)^3 and (-1 -sqrt(3)/3)^3 to help
simplify). None of the final simplified answers involves a cube root or
square root and one is an integer!
- Section 3.7: 1,2,3,4.
- Grading: 1.: 5 pts each if did, no grading. = 20 pts
2. 5pts if did, no grading = 5pts
3*. 15 points each, careful grade =45 pts
4*. careful grade #6 for 15pts, 5pts each if did other two but do not grade = 25pts
5. 5pts each if did, no grading = 10pts
6. 5pts if did, no grading = 5pts
7*. 15pts careful grade = 15pts
8. 10 pts if did, no grading = 10 pts
9. 5pts if did no grading = 5pts
10*. careful grade #2, #4 for 15pts each and 5pts each for other two do not careful grade = 40pts.
total=140
-
- Section 3.7: 1,2,3,4.
-
Solutions.
- Stats: Possible=; Median=; Max=; Min=.
- Homework 8: Due Dec. 9, 9:30am.
- Sec.3.7:8-12.
- Let p(x)=x^2 + x+1 in Q[x].
- Prove p is irreductible in Q[x].
- Let R=Q[x]/(p(x)) be the ring of congruence classes. By a
theorem, we know R is a field. Prove this directly by finding
a formula for the inverse of every non-zero congruence class.
That is, given [ax+b] not zero with a,b rational, find
the formula for [ax+b]^-1 in terms of a and b.
-
Use the previous part to find [x]^-1, [3x+1]^-1, [x+4]^-1, [x^8+1]^-1.
- Let p(x)=x^2 -4 in Q[x].
- Prove p is reductible in Q[x].
- Let R=Q[x]/(p(x)) be the ring of congruence classes. By a
theorem, we know R is not a field. Find
a formula for the inverse of a non-zero congruence class [ax+b], when it
exists. Use your formulas to determine which elements are units.
- Find polynomials f(x) and g(x) in Z_2[x] so that Z_2[x]/(f) is
a field of order 8 and Z_2[x]/(g) is a ring of order 8 with zero
divisors. Justify your answers.
- Grading:
- Solutions.
- Stats: Possible=; Median=; Max=; Min=.
Office Hours
who where when
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Dave Collingwood C545PDL M: 8:00-9:15am, F:10:30-noon, or appt.
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Sonali Tamhankar Math study center Th: 2-4pm, or appt.
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