Math & Nature Fish feeding mechanisms ◦ Suction feeding Goliath grouper Epinephelus itajara Questions What fluid velocity can the goliath grouper generate during suction feeding? How does suction feeding by the goliath grouper compare to other fish?

Math & Nature Suction feeding in the goliath grouper ◦ Given Dimensions of cones A and B at rest (t0) 1) Find the volume of the goliath grouper feeding mechanism at rest (t0). b c a a e d

Math & Nature Suction feeding in the goliath grouper ◦ Given Dimensions of cones A and B at rest (t0) 1) Find the volume of the goliath grouper feeding mechanism at rest (t0). c b a a e d

Math & Nature Suction feeding in the goliath grouper ◦ Given Dimensions of cones A and B at maximum expansion (t1) 2) Find the volume of the goliath grouper feeding mechanism at maximum expansion (t1).

Math & Nature Suction feeding in the goliath grouper ◦ Given Volume of the goliath grouper feeding mechanism at rest (t0) and at maximum expansion (t1) Duration of the feeding event (t1 - t0) Area of the mouth opening at maximum expansion (t1) 4) Find the velocity of water flow into the mouth of

Math & Nature References ◦ Bishop, K.L., Wainwright, P.C., and Holzman, R. (2008). Anterior to posterior wave of buccal expansion in suction feeding fish is critical for optimizing fluid flow velocity profile. Journal of the Royal Society, Interface. 5:1309-1316. ◦ Ferry-Graham, L.A., Wainwright, P.C., and Bellwood, D.R. (2001). Prey capture in long-jawed butterflyfishes (Chaetodontidae): the functional basis of novel feeding habits. Journal of Experimental Marine Biology and Ecology. 256:167-184. ◦ Galileo Galilei, The Assayer, as translated by Stillman Drake (1957), Discoveries and Opinions of Galileo pp. 237 - 238. New York: Doubleday & Company. ◦ Gibb, A.C. and Ferry-Graham, L.A. (2005). Cranial movements during suction feeding in teleost fishes: Are they modified to enhance suction production? Zoology. 108(2): 141-153. ◦ Grubich, J.R. (2001). Prey Capture in Actinopterygian Fishes: A Review of Suction Feeding Motor Patterns with New Evidence from an Elopomorph Fish, Megalops atlanticus. Integrative and Comparative Biology. 41(6): 1258-1265. ◦ Holzman, R., Day, S.W., and Wainwright, P.C. (2007). Timing is everything: coordination of strike kinematics affects the force exerted by suction feeding fish on attached prey. Journal of Experimental Biology. 210: 3328-3336. ◦ Holzman, R., Day, S.W., Mehta, R.S., and Wainwright, P.C. (2008). Jaw protrusion enhances forces exerted on prey by suction feeding fishes. Journal of the Royal Society, Interface. 5(29): 1445-1457.

Goliath Grouper Suction Feeding Cone A Length (mm) Area (mm2) a 34.9 N/A b 153.6 Cone B Length (mm) Area (mm2) a 34.9 Time 0 c 54.3 N/A d 6.4 e Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a N/A b Cone B Length (mm) Area (mm2) a Time 1 c d e Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3) Volume (mm3) Volume (mm3) Volume (mm3) 0.132

Goliath Grouper Suction Feeding Cone A Length (mm) Area (mm2) a 34.9 N/A b 153.6 Cone B Length (mm) Area (mm2) a 34.9 Time 0 c 54.3 N/A d 6.4 e 12.2 Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a N/A b Cone B Length (mm) Area (mm2) a Time 1 c d e Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3) 195916.8 Volume (mm3) 84289.7 180206.5 Volume (mm3) Volume (mm3) 0.132

Goliath Grouper Suction Feeding Cone A Length (mm) Area (mm2) a 34.9 N/A b 153.6 Cone B Length (mm) Area (mm2) a 34.9 Time 0 c 54.3 N/A d 6.4 e 12.2 Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a 39.5 N/A b 161.3 Cone B Length (mm) Area (mm2) a 39.5 Time 1 c 56.4 d 32.6 e Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3) 195916.8 Volume (mm3) 84289.7 280206.5 Volume (mm3) Volume (mm3) 0.132

Goliath Grouper Suction Feeding Cone A Length (mm) Area (mm2) a 34.9 N/A b 153.6 Cone B Length (mm) Area (mm2) a 34.9 Time 0 c 54.3 N/A d 6.4 e 12.2 Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a 39.5 N/A b 161.3 Cone B Length (mm) Area (mm2) a 39.5 Time 1 c 56.4 d 32.6 e 266.5 Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3) 195916.8 Volume (mm3) 84289.7 280206.5 Volume (mm3) 263547.1 Volume (mm3) 230974.7 494521.7 214315.3 0.132

Goliath Grouper Suction Feeding Cone A Length (mm) Area (mm2) a 34.9 N/A b 153.6 Cone B Length (mm) Area (mm2) a 34.9 Time 0 c 54.3 N/A d 6.4 e 12.2 Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a 39.5 N/A b 161.3 Cone B Length (mm) Area (mm2) a 39.5 Time 1 c 56.4 3338.8 d 32.6 e 266.5 Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3) 195916.8 Volume (mm3) 84289.7 280206.5 Volume (mm3) 263547.1 Volume (mm3) 230974.7 494521.7 214315.3 0.132 3338.8

Goliath Grouper Suction Feeding Cone A Length (mm) Area (mm2) a 34.9 N/A b 153.6 Cone B Length (mm) Area (mm2) a 34.9 Time 0 c 54.3 N/A d 6.4 e 12.2 Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a 39.5 N/A b 161.3 Cone B Length (mm) Area (mm2) a 39.5 Time 1 c 56.4 3338.8 d 32.6 e 266.5 Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3) 195916.8 Volume (mm3) 84289.7 280206.5 Volume (mm3) 263547.1 Volume (mm3) 230974.7 494521.7 214315.3 0.132 3338.8 486

Math & Nature Suction feeding in the goliath grouper ◦ Given Dimensions of cone B at maximum expansion (t1) 3) Find the area of the goliath grouper mouth at maximum expansion (t1). A. Collins mouth

Math & Nature Suction feeding in the snook Centropomus undecimalis ◦ Given Dimensions of cones A and B at rest (t0) and at maximum expansion of the feeding mechanism (t1) Duration of the feeding event (t1 - t0) 5) Find the velocity of water flow into the mouth of the snook during suction feeding.

Math & Nature Suction feeding in the longjaw butterfly fish Forcipiger longirostris ◦ Given Dimensions of cones A and B at rest (t0) and at maximum expansion of the feeding mechanism (t1) Duration of the feeding event (t1 - t0) 6) Find the velocity of water flow into the mouth of the longjaw butterfly fish during suction feeding.

PLACEMENT HOW? Placement Placement Test Test Transfer Transfer Credits Credits SAT SAT or or ACT ACT Scores Scores High High School School AP AP Scores Scores (Mathematics) (Mathematics) WHAT TO DO? Take Take placement placement test test on on any any campus campus at at Testing Testing Center. Center. Accuplacer Accuplacer MATH MATH can can be be taken taken twice. twice. Students Students who who wish wish higher higher placement placement must must then then “appeal”. “appeal”. Appeal Appeal is is request to take a pencil-and-paper type test on material from the course they request to take a pencil-and-paper type test on material from the course they placed placed into. into. Bring Bring transcript transcript showing showing general general education education math math credits credits from from another another college college or or university university to to CCBC CCBC for for evaluation. evaluation. If If completed completed in in Maryland, Maryland, the the highest highest level level developmental math course, Intermediate Algebra can be used for placement. developmental math course, Intermediate Algebra can be used for placement. Placement Placement by by SAT SAT MATH MATH score score of of 500 500 or or higher higher (or (or by by ACT ACT MATH MATH score score 21 21 or or higher) places the student into an entry-level general education math course higher) places the student into an entry-level general education math course (MATH (MATH 111, 111, 125, 125, 131/2/3, 131/2/3, 135, 135, 163). 163). For For higher higher placement, placement, the the student student must must take take Accuplacer MATH. MATH. Accuplacer Students Students with with documentation documentation of of AP AP math math scores scores of of 3, 3, 4, 4, or or 5 5 from from high high school school can can be awarded college credit and placement according to this chart. be awarded college credit and placement according to this chart.

Core Math MATH 95 MATH 96 MATH 126 MATH 176 MATH 96 MATH 126 MATH 176 MATH 126E MATH 176 Recommendation: If you start in Math 95 or Math 96 take summer classes to stay on track! MATH 126 MATH 176 MATH 181 or Math 182 will meet the College of Business math requirement. MATH 176 Pg. 12 of your Advising Manual

Math & Nature References ◦ Liem, K., Bemis, W., Walker, W.F., and Grande, L. (2001). Functional Anatomy of the Vertebrates: An Evolutionary Perspective. New York. Cengage Learning. ◦ Merrill, M.D. (2002). First principles of instruction. Educational Technology Research and Development. 50 (3): 43 – 59. ◦ Motta, P.J., Hueter, R.E., Tricas, T.C., Summers, A.P., Huber, D.R., Lowry, D., Mara, K.R., Matott, M.P., Whitenack, L.B., and Wintzer, A.P. (2008). Functional morphology of the feeding apparatus, feeding constraints, and suction performance in the nurse shark Ginglymostoma cirratum. Journal of Morphology. 269(9): 1041-1055. ◦ Motta, P.J., Maslanka, M., Hueter, R.E., Davis, R.L., de la Parra, R., Mulvany, S.L., Habegger, M.L., Strother, J.A., Mara, K.R., Gardiner, J.M., Tyminski, J.P., and Zeigler, L.D. (2010). Feeding anatomy, filter-feeding rate, and diet of whale sharks Rhincodon typus during surface ram filter feeding off the Yucatan Peninsula, Mexico. Zoology. 113: 199-212. ◦ Sanford, C.P.J. and Wainwright, P.C. (2002). Use of sonomicrometry demonstrates the link between prey capture kinematics and suction pressure in largemouth bass. Journal of Experimental Biology. 205: 3445-3457. ◦ Svanback, R., Wainwright, P.C., and Ferry-Graham, L.A. (2002). Linking cranial kinematics, buccal pressure, and suction feeding performance in largemouth bass. Physiological and Biochemical Zoology. 75(6): 532-543.

Snook Suction Feeding Cone A Length (mm) Area (mm2) a 2.1 N/A b 27.6 Cone B Length (mm) Area (mm2) a 2.1 Time 0 c 12.3 N/A d 1.8 e Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a 7.0 N/A b 28.9 Cone B Length (mm) Area (mm2) a 7.0 Time 1 c 12.3 d 5.9 e Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3) Volume (mm3) Volume (mm3) Volume (mm3) 0.036

Snook Suction Feeding Cone A Length (mm) Area (mm2) a 2.1 N/A b 27.6 Cone B Length (mm) Area (mm2) a 2.1 Time 0 c 12.3 N/A d 1.8 e 73.8 Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a 7.0 N/A b 28.9 Cone B Length (mm) Area (mm2) a 7.0 Time 1 c 12.3 109.4 d 5.9 e 66.0 Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3) 127.5 Volume (mm3) 147.2 274.7 Volume (mm3) 1482.9 Volume (mm3) 1611.5 3094.4 2819.7 0.036 109.4 716

Longjaw Butterfly Fish Suction Feeding Cone A Length (mm) Area (mm2) a 5.0 N/A b 14.9 Cone B Length (mm) Area (mm2) a 5.0 Time 0 c 31.2 N/A d 1.1 e Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a 5.0 N/A b 14.9 Cone B Length (mm) Area (mm2) a 5.0 Time 1 c 31.6 d 1.1 e Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3) Volume (mm3) Volume (mm3) Volume (mm3) 0.022

Longjaw Butterfly Fish Suction Feeding Cone A Length (mm) Area (mm2) a 5.0 N/A b 14.9 Cone B Length (mm) Area (mm2) a 5.0 Time 0 c 31.2 N/A d 1.1 e 8.8 Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a 5.0 N/A b 14.9 Cone B Length (mm) Area (mm2) a 5.0 Time 1 c 31.6 3.8 d 1.1 e 8.9 Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3) 390.1 Volume (mm3) 1036.0 1426.1 Volume (mm3) 390.1 Volume (mm3) 1049.3 1439.4 13.3 0.022 3.8 159

ACT SCORES PLACEMENT English 18 - 27 Engl 1010 Math 19 - 27 Math 1020/1810/1100 (check major) Math 28 + Credit given for Math 1020 SAT SCORES PLACEMENT Verbal 450 – 620 Engl 1010 Verbal 630 - 710 Credit given for Engl 1010 Verbal 720 + Credit given for Engl 1010 & 1020 Math 460 - 620 Math 1020/1810/1100 (check major) Math 630 + Credit given for Math 1020 COMPASS SCORES PLACEMENT Writing 68 + Engl 1010 Pre-Algebra 56 - 94 Math 1020 Algebra 36 – 88 Math 1020 College Algebra 30 - 66 Math 1020 Pre-Algebra 95+ Credit for Math 1020 Algebra 89+ Credit for Math 1020 College Algebra 67+ Credit for Math 1020

Math Study Skills Inventory Rate your achievement of the following statements by placing a 3 for almost always, 2 for sometimes, and 1 for almost never. If you have never even thought about doing what the statement says, put a 0. Selecting a math class _______ 1. I schedule my math class at a time when I am mentally sharp. _______ 2. When I register for a math class, I choose the best instructor for me. _______ 3. If I have a choice, I select a math class that meets three or four days a week instead of one or two. _______ 4. I schedule the next math class as soon as possible after I have completed the current course. _______ 5. I am sure that I have signed up for the correct level math course. Time and place for studying math _______ 6. I study math every day. _______ 7. I try to get my math homework immediately after math class. _______ 8. I have a specific time to study math. _______ 9. I have a specific place with few distractions to study math. ______ 10. I seek help with my math homework in the lab/tutoring center. ______ 11. I am careful to keep up to date with math homework. ______ 12. I study math at least 8 to 10 hours a week.

Math questions • Evaluate the following expressions: – – – – – – – Math.abs(-1.23) Math.pow(3, 2) Math.pow(10, -2) Math.sqrt(121.0) - Math.sqrt(256.0) Math.round(Math.PI) + Math.round(Math.E) Math.ceil(6.022) + Math.floor(15.9994) Math.abs(Math.min(-3, -5)) • Math.max and Math.min can be used to bound numbers. Consider an int variable named age. – What statement would replace negative ages with 0? – What statement would cap the maximum age to 40? 27

Topological Sort A topological sort of an acyclic directed graph orders the vertices so that if there is a path from vertex u to vertex v, then vertex v appears after vertex u MATH 120 One topological sort in the ordering. of the course prerequisite graph at left: MATH 150 MATH 224 ECE 282 CS 111 CS 150 ECE 381 CS 111, MATH MATH 152 120, CS 140, MATH 423 MATH 125, CS ECE 482 MATH 250 150, MATH 224, CS 234 CS 240 STAT 380 CS 234, CS 240, ECE 483 MATH 321 ECE 282, CS 312, CS 312 CS 321 CS 325, MATH CS 325 150, MATH 152, CS 482 STAT 380, CS 321, CS 340 MATH 250, MATH CS 382 CS 434 321, CS 314, CS 314 MATH 423, CS CS 330 340, CS 425, ECE CS 425 381, CS 434, ECE CS 447 482, CS 330, CS CS 423 382, CS 423, CS CS 499 CS 438 CS 456 438, CS 454, CS 447, CS 499, CS CS 454 482, CS 456, ECE MATH 125 CS 340 CS 140 Page 5

Stocks “Subject to Overfishing” (40) – as of September 30, 2010 New England: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Cod – Gulf of Maine Cod – Georges Bank Yellowtail flounder – Southern New England/Middle Atlantic Yellowtail flounder – Cape Cod/Gulf of Maine White Hake Winter Flounder – Georges Bank Winter Flounder – Southern New England/Middle Atlantic Windowpane - Gulf of Maine / Georges Bank Windowpane - Southern New England / Mid-Atlantic Witch Flounder - Northwestern Atlantic Coast Highly Migratory Species: Pacific: 1.Yellowfin Tuna – Eastern Pacific2 1. Blue Marlin – Atlantic2 2. White Marlin – Atlantic2 3. Sailfish – West Atlantic2 4. Albacore – North Atlantic2 5. Bluefin Tuna – West Atlantic2 6. Sandbar Shark 7. Dusky Shark 8. Blacknose Shark 9. Shortfin Mako - Atlantic Pacific and Western Pacific 1. Bigeye Tuna – Pacific2 2. Pacific bluefin tuna – Pacific2 South Atlantic: Gulf of Mexico: 1. Red Snapper 2. Greater Amberjack 3. Gag 4. Gray Triggerfish 1. Indicates non-FSSI stock U.S. Department of Commerce National Oceanic and Atmospheric Administration National Marine Fisheries Service Office of Sustainable Fisheries 2. Stock is fished by U.S. and International fleets. Blue = Also Overfished 1. Vermilion Snapper 2. Red Snapper 3. Snowy Grouper 4. Tilefish 5. Red Grouper 6. Black Sea Bass 7. Gag 8. Speckled Hind 9. Warsaw Grouper Caribbean: 1. Snapper Unit 1 2. Grouper Unit 1 3. Grouper Unit 4 4. Queen Conch 5. Parrotfishes1 11

Overfished Stocks (47) – as of September 30, 2010 New England: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. North Pacific: 1. Blue King Crab – Pribilof Islands Atlantic Cod – Georges Bank Yellowtail Flounder – Georges Bank Yellowtail Flounder – Southern New England/Middle Atlantic Yellowtail Flounder – Cape Cod/Gulf of Maine White Hake Winter Flounder - Southern New England / Mid-Atlantic Ocean Pout Atlantic Halibut Windowpane - Gulf of Maine / Georges Bank Winter flounder - Georges Bank Witch flounder - Northwestern Atlantic Coast Smooth Skate 14. Thorny Skate Atlantic Salmon1 15. Atlantic Wolffish - Gulf of Maine / Georges Bank1 Highly Migratory Species: 1. Blue Marlin – Atlantic2 2. White Marlin – Atlantic2 3. Albacore – North Atlantic2 4. Bluefin Tuna – West Atlantic2 5. Sandbar Shark Mid-Atlantic: 6. Porbeagle Shark 1. Butterfish (Atlantic) 7. Dusky Shark 8. Blacknose Shark ific: Cowcod Yelloweye Rockfish Canary rockfish - Pacific Coast Petrale sole – Pacific Coast Coho salmon - Washington Coast: Queets1 Coho salmon - Washington Coast: Western Strait of Juan de Fuca1 Chinook salmon - California Central Valley: Sacramento (fall)1 Gulf of Mexico: Western Pacific 3/27/19 1. Seamount Groundfish Complex – Hancock Seamount U.S. Department of Commerce National Oceanic and Atmospheric Administration South Atlantic: 1. Red Snapper 2. Greater Amberjack 3. Gray Triggerfish 4. Gag 1. Indicates non-FSSI stock 2. Stock is fished by U.S. and International fleets. 1. Pink Shrimp 2. Snowy Grouper 3. Black Sea Bass 4. Red Porgy 5. Red Snapper 6. Red Grouper Caribbean: 1. Grouper Unit 1 2. Grouper Unit 2 3. Grouper Unit 4 4. Queen Conch National Marine Fisheries Service Office of Sustainable Fisheries 13

Biological Neural Net Example : Human Eye retina fovea rods • • • • • • • • • • • cones lens optic Eye is ………………. of brain – powerful bio-electrochemical computer nerve Light enters thru ……and focuses on …….. (similar to photographic film) Retina is dense matrix of photoreceptors – ………………………………. Rods – form ……… images in dim light 100X more sensitive than cones Cones handle …………….., 4X faster than rods in response to light Rods, Cones convert light to electric signals, total 130million, 6% cones Highest conc of cones is in ……….., 1.5mm diameter, 2000 cones Retinal neurons arranged in layers receive electric signals via synapses Pre-processing of image takes place at retinal level in neuron network Signals arrive at …………….(1 million), axons of which form …………. Optic nerve fibers terminate in lateral geniculate nucleus LGN in brain