Blackboard Shots with Prefix "15-475"

150420-143416: Feb 24 Problem 1.

150331-190552: March 26 Handout Problem 4 (2).

150331-190541: March 26 Handout Problem 4.

150331-190533: March 26 Handout Problem 6.

150331-190523: March 26 Handout Problem 1 (3).

150331-190514: March 26 Handout Problem 1 (2).

150331-190508: March 26 Handout Problem 1.

150326-171644: March 26 Handout hints (4).

150326-171640: March 26 Handout hints (3).

150326-171634: March 26 Handout hints (2).

150326-171630: March 26 Handout hints.

150326-171623: Quiz 10 problem 3 (2).

150326-171618: Quiz 10 problem 3.

150324-163110: March 19 handout, Problem 5 solution by Bill.

150324-163108: Row and column reduction over the integers (2).

150324-163107: Row and column reduction over the integers.

150324-163105: Can you swap two memory cells without using a third? (2)

150324-163103: Can you swap two memory cells without using a third?

150319-163345: Infinitely many prisoners on an island...

150319-163341: March 19 Problem 2 (2).

150319-163336: March 19 Problem 2.

150319-163333: March 19 Problem 3.

150319-163328: March 19 Problem 4.

150319-163323: Cheating women in a village.

150319-163319: Left-right-left-right and in-out-in-out.

150317-163316: Packing 125 $4\times2\times1$ boxes in a $10\times10\times10$ cube.

150317-163315: A classic first-year algebra problem.

150317-163314: Quiz 9 Problems 1 and 3.

150312-213623: March 12 Problem 0: The density of $n\alpha$ (2).

150312-213619: March 12 Problem 0: The density of $n\alpha$.

150312-213614: March 12 Problem 4: Symmetric Latin squares.

150312-213610: March 12 Problem 7: $(\sigma_1-1)(\sigma_2-2)\cdots(\sigma_n-n)$.

150312-213608: March 12 Problem 10: Harmonic sums are never integers.

150312-213604: Samer earns $5! (2)

150312-213602: Samer earns $5!

150312-213558: March 12 Problem 9: The $x+y$ trailer problem.

150312-213556: March 12 Problem 2: On chessboards.

150312-213551: March 12 Problem 5: Prisoners in a row.

150310-171912: Ramsey's theorem (2).

150310-171911: Ramsey's theorem.

150310-171909: Quiz 8 Problem 1.

150310-171908: Back to bread-slicing.

150305-182559: Ramsey theory (5).

150305-182555: Ramsey theory (4).

150305-182550: Ramsey theory (3).

150305-182547: Ramsey theory (2).

150305-182543: Ramsey theory.

150305-182540: Larson's 1.9.1, $ax^2+bx+c=0$ with odd $a,b,c$ (2).

150305-182536: Larson's 1.9.1, $ax^2+bx+c=0$ with odd $a,b,c$.

150305-182531: Tug of War (2).

150305-182528: Tug of War.

150305-182523: There are irrational $a$, $b$ s.t. $a^b$ is rational.

150305-182519: $\sqrt[n]{2}$ is irrational.

150303-173807: Quiz 7 Problem 1, after-class discussion.

150303-173806: Quiz 7 Problem 1 continued.

150303-173805: Quiz 7 Problem 2 and Problem 1.

150303-173804: Quiz 7 Problem 2.

150226-165649: Pigeonhole: Larson's problem 2.6.10.

150226-165648: Pigeonhole: Larson's problem 2.6.1 (2).

150226-165647: Pigeonhole: Larson's problem 2.6.1.

150226-165646: The scissors jack problem (2).

150226-165644: The scissors jack problem.

150226-165643: Rook arrangements (3).

150226-165642: Rook arrangements (2).

150226-165641: Rook arrangements.

150226-165640: A problem related to the isoperimetric inequality.

150224-180040: Quiz 6 discussion (3).

150224-180039: Quiz 6 discussion (2).

150224-180037: Quiz 6 discussion.

150212-170501: $F(x)F(y)-F(xy)=x+y$.

150212-170459: The fundamental domain of $GG$.

150212-170458: The viewing angle of a chord (3).

150212-170456: The viewing angle of a chord (2).

150212-170454: The viewing angle of a chord.

150212-170453: The fundamental domain of $0$.

150212-170451: The isoperimetric inequallity (2).

150212-170449: The isoperimetric inequallity.

150212-170448: Quiz 5 Problem 3.

150212-170446: Quiz 5 Problem 2.

150212-170445: Quiz 5 Problem 1.

150210-161918: Cubics, areas, and symmetry groups of the plane.

150210-161917: Colouring the points of the plane.

150210-161916: Menu and $50 bounty!

150205-171728: Handout problems 6 and 7.

150205-171727: Legos on a disk.

150205-171726: The Kauffman bracket (5).

150205-171725: The Kauffman bracket (4).

150205-171724: The Kauffman bracket (3).

150205-171723: The Kauffman bracket (2).

150205-171722: The Kauffman bracket.

150205-171720: Folding and the perimeter.

150205-171719: Diagonals in a dodecadon (2).

150205-171718: Diagonals in a dodecadon.

150203-162705: Quiz 4 Problem 1: Snow plowing.

150203-162704: Quiz 4 Problem 2: Primes and squares mod 8 (2).

150203-162703: Quiz 4 Problem 2: Primes and squares mod 8.

150129-174022: Larson's 1.5.3.

150129-174021: Poles, guys, Ohm's law.

150129-174019: $a_{n+1}=\sqrt{\frac{1+a_n}{2}}$ (2).

150129-174018: $a_{n+1}=\sqrt{\frac{1+a_n}{2}}$.

150129-174017: Volumes of spheres (2).

150129-174016: Volumes of spheres.

150129-174015: Computing $\int e^{-x^2}dx$ (3).

150129-174014: Computing $\int e^{-x^2}dx$ (2).

150129-174012: Computing $\int e^{-x^2}dx$.

150127-163620: $x^2+y^2+z^2=2xyz$.

150127-163619: Solution of Quiz 3.

150127-163618: The Chinese Rings.

150122-171513: Ian earns $5.

150122-171512: The Sicherman dice (3).

150122-171511: The Sicherman dice (2).

150122-171510: The Sicherman dice.

150122-171509: Larson's 1.3.3 (2).

150122-171507: Larson's 1.3.3.

150122-171506: Solving $x^4+x^3+x^2+x+1=0$ (2).

150122-171505: Solving $x^4+x^3+x^2+x+1=0$.

150122-171504: Generating functions and the Fibonnaci numbers.

150122-171503: Integrating $\frac{1}{1-x^2}$.

150120-170151: The game of 15 (2).

150120-170150: The game of 15.

150120-170149: Quiz 2 solutions.

150120-170148: Admin.

150115-181440: Economic growth seen slowing (3).

150115-181439: Economic growth seen slowing (2).

150115-181438: Economic growth seen slowing.

150115-181437: Hieroglyphics.

150115-181436: $\lfloor\frac{a}{b}\rfloor+\lfloor\frac{2a}{b}\rfloor+\cdots+\lfloor\frac{(b-1)a}{b}\rfloor=\frac{(a-1)(b-1)}{2}$ (2).

150115-181435: $\lfloor\frac{a}{b}\rfloor+\lfloor\frac{2a}{b}\rfloor+\cdots+\lfloor\frac{(b-1)a}{b}\rfloor=\frac{(a-1)(b-1)}{2}$.

150115-181434: The Othello problem.

150115-181432: Two poles and a bird (2).

150115-181431: Two poles and a bird.

150115-181430: $\sum_{k=0}^n\binom{n}{k}^2 = \binom{2n}{n}$ (2).

150115-181429: $\sum_{k=0}^n\binom{n}{k}^2 = \binom{2n}{n}$.

150115-181428: A spherical loaf of bread (3)...

150115-181426: A spherical loaf of bread (2)...

150115-181425: A spherical loaf of bread...

150115-181423: Four cars in the Sahara desert (2).

150115-181422: Four cars in the Sahara desert.

150113-161950: Ants along a hoop.

150113-161949: The inequality of the means (2).

150113-161947: The inequality of the means.

150113-161946: Young's inequality, 1.

150113-161945: Young's inequality, 2.

150108-172839: A funny system of algebraic rules.

150108-172838: Quandles.

150108-172837: Given a sum of integers, maximize their product (2).

150108-172836: Given a sum of integers, maximize their product.

150108-172834: Next quiz.

150108-172833: $S_{n,0}$ using roots of unity (2).

150108-172831: $S_{n,0}$ using roots of unity.

150106-163010: $S_{n,0}$, $S_{n,1}$, and $S_{n,2}$ (4).

150106-163007: $S_{n,0}$, $S_{n,1}$, and $S_{n,2}$ (3).

150106-163003: $S_{n,0}$, $S_{n,1}$, and $S_{n,2}$ (2).

150106-162959: $S_{n,0}$, $S_{n,1}$, and $S_{n,2}$.

150106-162955: Course info.