How to Count like a Mathematician Counting Warmup Round 1 squares - - PowerPoint PPT Presentation
How to Count like a Mathe- matician Lara Pudwell Introduction How to Count like a Mathematician Counting Warmup Round 1 squares Lara Pudwell dominoes Round 2 trees Department of Mathematics and Computer Science blocks The Bigger
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Lara Pudwell
Department of Mathematics and Computer Science
VERUM Seminar June 7, 2013
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
What do you research?
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
What do you research?
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
So you think you can count?
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
So you think you can count?
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
You’ve already got some tricks up your sleeve.... How many dots do you see?
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
You’ve already got some tricks up your sleeve.... How many dots do you see? 6 + 5 + 6
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
You’ve already got some tricks up your sleeve.... How many dots do you see? 6 + 5 + 6 = 17 Trick 1: Break your counting job into smaller jobs and add those results.
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
You’ve already got some tricks up your sleeve.... How many dots do you see?
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
You’ve already got some tricks up your sleeve.... How many dots do you see? 7 · 6
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
You’ve already got some tricks up your sleeve.... How many dots do you see? 7 · 6 = 42 Trick 2: Multiplying speeds things up!
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
You’ve already got some tricks up your sleeve.... How many dots do you see?
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
You’ve already got some tricks up your sleeve.... How many dots do you see? 7 · 6
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
You’ve already got some tricks up your sleeve.... How many dots do you see? 7 · 6 − 3 42 − 3 = 39 Trick 3: Count a larger set and subtract off the extras.
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Thinking in black and white You have black squares and white squares . How many ways can you arrange a line of squares? 1 square? 2 ways
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Thinking in black and white You have black squares and white squares . How many ways can you arrange a line of squares? 1 square? 2 ways 2 squares? 4 ways
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Thinking in black and white You have black squares and white squares . How many ways can you arrange a line of squares? 1 square? 2 ways 2 squares? 4 ways 3 squares? 8 ways
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Thinking in black and white You have black squares and white squares . How many ways can you arrange a line of squares? 1 square? 2 ways 2 squares? 4 ways 3 squares? 8 ways What’s the pattern?
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Thinking in black and white You have black squares and white squares . How many ways can you arrange a line of squares? 1 square? 2 ways 2 squares? 4 ways 3 squares? 8 ways What’s the pattern? Count (end in ) + (end in ).
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Thinking in black and white You have black squares and white squares . How many ways can you arrange a line of squares? 1 square? 2 ways 2 squares? 4 ways 3 squares? 8 ways What’s the pattern? Count (end in ) + (end in ). (end in ) = (end in ) = (lines with one less square).
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Thinking in black and white You have black squares and white squares . How many ways can you arrange a line of squares? 1 square? 2 ways 2 squares? 4 ways 3 squares? 8 ways What’s the pattern? Count (end in ) + (end in ). (end in ) = (end in ) = (lines with one less square). Lines of length a = 2 × (lines of length a − 1)
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Thinking in black and white You have black squares and white squares . How many ways can you arrange a line of squares? 1 square? 2 ways 2 squares? 4 ways 3 squares? 8 ways What’s the pattern? Count (end in ) + (end in ). (end in ) = (end in ) = (lines with one less square). Lines of length a = 2 × (lines of length a − 1) length 1 2 3 4 5 6 7 8 # of arrangements 2 4 8 16 32 64 128 256
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Thinking in black and white What if you can’t have two black squares in a row? 1 square? 2 ways
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Thinking in black and white What if you can’t have two black squares in a row? 1 square? 2 ways 2 squares? 3 ways
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Thinking in black and white What if you can’t have two black squares in a row? 1 square? 2 ways 2 squares? 3 ways 3 squares? 5 ways What’s the pattern?
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Thinking in black and white What if you can’t have two black squares in a row? 1 square? 2 ways 2 squares? 3 ways 3 squares? 5 ways What’s the pattern? Count (end in ) + (end in ).
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Thinking in black and white What if you can’t have two black squares in a row? 1 square? 2 ways 2 squares? 3 ways 3 squares? 5 ways What’s the pattern? Count (end in ) + (end in ). (end in ) = (end in ) = (lines with two less squares) (end in ) = (lines with one less square).
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Thinking in black and white What if you can’t have two black squares in a row? 1 square? 2 ways 2 squares? 3 ways 3 squares? 5 ways What’s the pattern? Count (end in ) + (end in ). (end in ) = (end in ) = (lines with two less squares) (end in ) = (lines with one less square). Lines of length a = (lines of length a − 2) + (lines of length a − 1) length 1 2 3 4 5 6 7 8 # of arrangements 2 3 5 8 13 21 34 55
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Dominoes! You have a pile of dominoes . You wish to cover a rectangle of height 2 with non-overlapping dominoes. How many ways can this be done? 2 × 1 1 way
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Dominoes! You have a pile of dominoes . You wish to cover a rectangle of height 2 with non-overlapping dominoes. How many ways can this be done? 2 × 1 1 way 2 × 2 2 ways
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Dominoes! You have a pile of dominoes . You wish to cover a rectangle of height 2 with non-overlapping dominoes. How many ways can this be done? 2 × 1 1 way 2 × 2 2 ways 2 × 3 3 ways
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Dominoes! You have a pile of dominoes . You wish to cover a rectangle of height 2 with non-overlapping dominoes. How many ways can this be done? 2 × 1 1 way 2 × 2 2 ways 2 × 3 3 ways 2 × 4 5 ways Hmmm....
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Haven’t we met before? 2 3 5
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Haven’t we met before? 2 3 5 Replace: → and → → → →
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Haven’t we met before? 2 3 5 Replace: → and → → → → → → → ...then delete that last (white) box.
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Trees?
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Trees?
David Priscilla Kris Lara Ryan Dave Heather Amy Debbee Jennifer Lisa Jonathan Priscilla Rachel
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Trees we can actually count... Trees grow down from the top of the page. Each node in a tree either has 0 children or 2 children. Nodes with 0 children are called leaves. This tree has 11 nodes. 6 of them are leaves.
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Tree counting... leaves trees 1 1
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Tree counting... leaves trees 1 1 2 1
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Tree counting... leaves trees 1 1 2 1 3 2
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Tree counting... leaves trees 1 1 2 1 3 2 4 5 leaves 1 2 3 4 5 trees 1 1 2 5 ?
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Decomposing trees → ×
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Decomposing trees... So for the 4 leaf trees... → × 3 left leaves, 1 right → × → × 2 left leaves, 2 right → × 1 left leaf, 3 right → ×
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Decomposing trees... So for the 4 leaf trees... → × 3 left leaves, 1 right → × → × 2 left leaves, 2 right → × 1 left leaf, 3 right → × If Tn is the number of trees with n leaves... T4 = T3T1 + T2T2 + T1T3 = 2 · 1 + 1 · 1 + 1 · 2 = 2 + 1 + 2 = 5
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Tree enumeration leaves 1 2 3 4 5 6 7 trees 1 1 2 5 ? ? ? T4 = T3T1 + T2T2 + T1T3 = 2 · 1 + 1 · 1 + 1 · 2 = 2 + 1 + 2 = 5
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Tree enumeration leaves 1 2 3 4 5 6 7 trees 1 1 2 5 14 ? ? T4 = T3T1 + T2T2 + T1T3 = 2 · 1 + 1 · 1 + 1 · 2 = 2 + 1 + 2 = 5 Similarly... T5 = 5 · 1 + 2 · 1 + 1 · 2 + 1 · 5 = 14
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Tree enumeration leaves 1 2 3 4 5 6 7 trees 1 1 2 5 14 42 ? T4 = T3T1 + T2T2 + T1T3 = 2 · 1 + 1 · 1 + 1 · 2 = 2 + 1 + 2 = 5 Similarly... T5 = 5 · 1 + 2 · 1 + 1 · 2 + 1 · 5 = 14 T6 = 14 · 1 + 5 · 1 + 2 · 2 + 1 · 5 + 1 · 14 = 42
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Tree enumeration leaves 1 2 3 4 5 6 7 trees 1 1 2 5 14 42 132 T4 = T3T1 + T2T2 + T1T3 = 2 · 1 + 1 · 1 + 1 · 2 = 2 + 1 + 2 = 5 Similarly... T5 = 5 · 1 + 2 · 1 + 1 · 2 + 1 · 5 = 14 T6 = 14 · 1 + 5 · 1 + 2 · 2 + 1 · 5 + 1 · 14 = 42 T7 = 42 · 1 + 14 · 1 + 5 · 2 + 2 · 5 + 1 · 14 + 1 · 42 = 132
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
One last game... Pile 1 is sorted (largest blocks at the bottom). Piles 2 and 3 can be in any order. You can move blocks from left to right. Question: How many possible arrangements can be made in Pile 3? Pile 1 Pile 2 Pile 3
5 4 3 2 1
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
One last game... Pile 1 is sorted (largest blocks at the bottom). Piles 2 and 3 can be in any order. You can move blocks from left to right. Question: How many possible arrangements can be made in Pile 3? Pile 1 Pile 2 Pile 3
5 4 3 2 1
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
One last game... Pile 1 is sorted (largest blocks at the bottom). Piles 2 and 3 can be in any order. You can move blocks from left to right. Question: How many possible arrangements can be made in Pile 3? Pile 1 Pile 2 Pile 3
5 4 3 2 1
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
One last game... Pile 1 is sorted (largest blocks at the bottom). Piles 2 and 3 can be in any order. You can move blocks from left to right. Question: How many possible arrangements can be made in Pile 3? Pile 1 Pile 2 Pile 3
5 4 3 2 1
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
One last game... Pile 1 is sorted (largest blocks at the bottom). Piles 2 and 3 can be in any order. You can move blocks from left to right. Question: How many possible arrangements can be made in Pile 3? Pile 1 Pile 2 Pile 3
5 4 2 3 1
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
One last game... Pile 1 is sorted (largest blocks at the bottom). Piles 2 and 3 can be in any order. You can move blocks from left to right. Question: How many possible arrangements can be made in Pile 3? Pile 1 Pile 2 Pile 3
5 4 2 1 3
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
One last game... Pile 1 is sorted (largest blocks at the bottom). Piles 2 and 3 can be in any order. You can move blocks from left to right. Question: How many possible arrangements can be made in Pile 3? Pile 1 Pile 2 Pile 3
5 2 4 1 3
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
One last game... Pile 1 is sorted (largest blocks at the bottom). Piles 2 and 3 can be in any order. You can move blocks from left to right. Question: How many possible arrangements can be made in Pile 3? Pile 1 Pile 2 Pile 3
2 4 5 1 3
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
One last game... Pile 1 is sorted (largest blocks at the bottom). Piles 2 and 3 can be in any order. You can move blocks from left to right. Question: How many possible arrangements can be made in Pile 3? Pile 1 Pile 2 Pile 3
2 4 1 3 5
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
One last game... Pile 1 is sorted (largest blocks at the bottom). Piles 2 and 3 can be in any order. You can move blocks from left to right. Question: How many possible arrangements can be made in Pile 3? Pile 1 Pile 2 Pile 3
2 1 3 5 4
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
One last game... Pile 1 is sorted (largest blocks at the bottom). Piles 2 and 3 can be in any order. You can move blocks from left to right. Question: How many possible arrangements can be made in Pile 3? Pile 1 Pile 2 Pile 3
1 3 5 4 2
One possible arrangement: 24531
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Counting piles... 1
11
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Counting piles... 1
11 2
1 2 1 2
2
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Counting piles... 1
11 2
1 2 1 2
2 3
3 2 1 2 3 1 1 3 2 2 1 3 1 2 3
5
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Counting piles... 1
11 2
1 2 1 2
2 3
3 2 1 2 3 1 1 3 2 2 1 3 1 2 3
5
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Counting piles... 1
11 2
1 2 1 2
2 3
3 2 1 2 3 1 1 3 2 2 1 3 1 2 3
5
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
D` ej´ a vu?
1→
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
D` ej´ a vu?
1→ Otherwise, locate the smallest block. Blocks above → left subtree. Blocks below → right subtree.
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
D` ej´ a vu?
1→ Otherwise, locate the smallest block. Blocks above → left subtree. Blocks below → right subtree.
1 2
→
1 2
→
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
D` ej´ a vu?
1→ Otherwise, locate the smallest block. Blocks above → left subtree. Blocks below → right subtree.
1 2
→
1 2
→
1 2 3 1 3 2 2 1 3 2 3 1 3 2 1
↓ ↓ ↓ ↓ ↓
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
One last trick...
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
One last trick...
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
What else is out there?
1 1 1 −1 1 1
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Plane partitions
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Plane partitions
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Plane partitions
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Plane partitions
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Plane partitions
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Counting problems!
1 3 5 4 2
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
Why?
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
What is it good for? G.H. Hardy (1877-1947)
“Hardy”, March 20, 2013 via http://www-groups.dcs.st-and.ac.uk/ ~history/PictDisplay/Hardy.html, public domain.
A Mathematician’s Apology (1940)
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
What is it good for? G.H. Hardy (1877-1947)
“Hardy”, March 20, 2013 via http://www-groups.dcs.st-and.ac.uk/ ~history/PictDisplay/Hardy.html, public domain.
A Mathematician’s Apology (1940) “No discovery of mine has made, or is likely to make... the least difference to the amenity of the world.”
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?
What is it good for?
“Impure Mathematics”, March 20, 2013 via http://abstrusegoose.com/504, Creative Commons Attribution-Noncommercial.
How to Count like a Mathe- matician Lara Pudwell Introduction Counting Warmup Round 1
squares dominoes
Round 2
trees blocks
The Bigger Picture So what do you research?