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.

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 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.

Math & Nature References ◦ Van Wassenbergh, S., Herrel, A., Adriaens, D., and Aerts, P. (2007). No trade-off between biting and suction feeding performance in clariid catfishes. Journal of Experimental Biology. 210: 27-36. ◦ Wainwright, P.C., Huskey, S.H., Turingan, R.G., and Carroll, A.M. (2006). Ontogeny of suction feeding capacity in snook, Centropomis undecimalis. Journal of Experimental Zoology. 305A: 246-252.

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

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

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

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?

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

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 & Nature Suction feeding ◦ Given Velocities of water flow into the mouths of all three fish 7) Determine which fish is the best suction feeder. Korhnak v(t) = 486 mm/sec v(t) = 716 mm/sec v(t) = 159 mm/sec

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.

Programs: (see graduate handbook for details) M.S. program: 27-33 credit hours, thesis, exams, project depending on option Required for all options: Advanced Calculus (Math 451) Real Analysis (Math 551) and Linear Algebra (Math 543) Can place out of these via Basic Exam if you have equivalent background Courses offered on a yearly basis : Math 541-641 Algebra Math 551-651 Real Analysis Math 581-681 Topology Math 521-522 Numerical Analysis Math 563 Modeling Math 564 Differential Equations (spring) Math 543 Linear Algebra (spring) Math 567-568 Advanced calculus for engineering/sci students Math 571 Combinatorics (spring this year) Math 573 Graph theory (fall this year) (second semester of Graph Theory & Combinatorics depends on enrollment and level of students) Exams: M.S. Advanced Exam (for option A & C) Two areas from Algebra, Real Analysis, Topology, Differential Equations Option B: Industrial/Applied mathematics – 33 hrs + project Mathematics for Secondary Educators option – 33 hours + exams

40 Tentative List of Courses for Graduate CEEN Students Mathematics and Statistics: MATH 415 Modern Algebra I* MATH 416 Modern Algebra II MATH 446 Principles of Analysis I* MATH 447 Topics in Analysis II STAT 601 Statistical Analysis MATH 606 Theory of Probability I MATH 607 Real Variables I* MATH 608 Real Variables II MATH 619 - Applied Probability* MATH 625 - Applied SDEs MATH 651 Optimization I* MATH 630 – Combinatorics MATH 652

Understanding your Math assessment scores Math Test Math Score Math Course Taken Trigonometry Recommendation 44 or higher College Algebra 43 or higher Math 071 & Math 62 Math 021*, 22*, 51, 52*, 61, 63 (also requires geometry) Algebra 33 or higher Math 013 Pre-Algebra 34 or higher Math 111 21-33 0-33 Math 311 Math 310 and/or Math 014

MELT program curriculum map with information about courses in which each learning outcome and performance indicator is (a) first introduced, (b) reinforced (c) reinforced and assessed Course Learning Outcome 1 Learning Outcome 2 P 1.1 P 1.2 P 1.3 P 2.1 P 2.2 P 2.3 P 2.4 a a b/c a a b/c a a b/c a a a a MATH 2031 Number Systems and Operations for Teachers b/c b/c b/c b/c b/c b/c b/c MATH 2032 Algebra and Geometry for Teachers b/c b/c b/c b/c b/c b/c b/c MATH 2350 Foundations of Mathematics b/c b/c b/c MATH 3100 Linear Algebra and Matrix Theory b/c b/c b/c MATH 4310 History of Mathematical Ideas a a a MATH 4320 Theory of Numbers b/c b/c b/c MATH 4420 Foundations of Geometry b/c b/c b/c MATH 4630 Mathematical Modeling and Analysis a a a MATH 4720 Statistical Methods c c c a b a MATH 1450 Calculus 1 MATH 1451 Calculus 2 MATH 2030 Problem Solving and Reasoning for Teachers