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This commit is contained in:
2025-09-24 22:02:23 -07:00
parent 69d835a2d2
commit 0b7acaf5ae
8 changed files with 31 additions and 54 deletions

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@ -31,7 +31,9 @@ Rewrite the following binary decimals in base 10: \
#definition(label: "floatbits")
Another way we can interpret a bit string is as a _signed floating-point decimal_, or a `float` for short. \
Floats represent a subset of the real numbers, and are interpreted as follows: \
#note([The following only applies to floats that consist of 32 bits. We won't encounter any others today.])
#note(
[The following only applies to floats that consist of 32 bits. We won't encounter any others today.],
)
#align(center, box(inset: 2mm, cetz.canvas({
import cetz.draw: *

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@ -134,14 +134,7 @@ Fill the following tropical addition and multiplication tables
table(
columns: (col, col, col, col, col, col),
align: center,
table.header(
[$#tp$],
[$1$],
[$2$],
[$3$],
[$4$],
[$#sym.infinity$],
),
table.header([$#tp$], [$1$], [$2$], [$3$], [$4$], [$#sym.infinity$]),
box(inset: 3pt, $1$), [], [], [], [], [],
box(inset: 3pt, $2$), [], [], [], [], [],
@ -152,14 +145,7 @@ Fill the following tropical addition and multiplication tables
table(
columns: (col, col, col, col, col, col),
align: center,
table.header(
[$#tm$],
[$0$],
[$1$],
[$2$],
[$3$],
[$4$],
),
table.header([$#tm$], [$0$], [$1$], [$2$], [$3$], [$4$]),
box(inset: 3pt, $0$), [], [], [], [], [],
box(inset: 3pt, $1$), [], [], [], [], [],
@ -178,14 +164,7 @@ Fill the following tropical addition and multiplication tables
table(
columns: (col, col, col, col, col, col),
align: center,
table.header(
[$#tp$],
[$1$],
[$2$],
[$3$],
[$4$],
[$#sym.infinity$],
),
table.header([$#tp$], [$1$], [$2$], [$3$], [$4$], [$#sym.infinity$]),
box(inset: 3pt, $1$),
box(inset: 3pt, $1$),
@ -225,14 +204,7 @@ Fill the following tropical addition and multiplication tables
table(
columns: (col, col, col, col, col, col),
align: center,
table.header(
[$#tm$],
[$0$],
[$1$],
[$2$],
[$3$],
[$4$],
),
table.header([$#tm$], [$0$], [$1$], [$2$], [$3$], [$4$]),
box(inset: 3pt, $0$),
box(inset: 3pt, $0$),
@ -281,8 +253,7 @@ Adjacent parenthesis imply tropical multiplication
#solution([
$
(x #tp 2)(x #tp 3)
&= x^2 #tp 2x #tp 3x #tp (2 #tm 3) \
(x #tp 2)(x #tp 3) & = x^2 #tp 2x #tp 3x #tp (2 #tm 3) \
& = x^2 #tp (2 #tp 3)x #tp (2 #tm 3) \
& = x^2 #tp 2x #tp 5
$

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@ -12,7 +12,9 @@ There are four classes of Euclidean isometries:
- reflections
- rotations
- glide reflections
#note([We can prove there are no others, but this is beyond the scope of this handout.]) \
#note(
[We can prove there are no others, but this is beyond the scope of this handout.],
) \
A simple example of each isometry is shown below:
#let demo(c) = {

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@ -17,7 +17,9 @@ Maximize the product $a_1 #sym.times a_2 #sym.times ... #sym.times a_k$
Of course, all $a_i$ should be greater than $1$. \
Also, all $a_i$ should be smaller than four, since $x <= x(x-2)$ if $x >= 4$. \
Thus, we're left with sequences that only contain 2 and 3. \
#note([Note that two twos are the same as one four, but we exclude fours for simplicity.])
#note(
[Note that two twos are the same as one four, but we exclude fours for simplicity.],
)
#v(2mm)