Math & Nature The universe is written in the language of mathematics ◦ Galileo Galilei, 1623 Quantitative analysis of natural phenomena is at the heart of scientific inquiry Nature provides a tangible context for mathematics instruction

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.

Example: Foundational Degree Requirements Communication - Oral: Recognize, send, and respond to communications for varied audiences both as speaker and listener. (LEAP Communication) (State Board Core, Communication) (HS Language Arts - Speech) Complete 3 credits ____ COMM 101 Critical/Creative Thinking and Problem Solving: Engage and demonstrate the ability to analyze and evaluate information and arguments; select or design appropriate frameworks and strategies to solve problems in multiple contexts individually and collaboratively. (LEAP Critical and Creative thinking) (Across the curriculum) (HS Humanities/Fine Arts/Interdisciplinary) Complete 3 credits. ____ ENGL 175 Introduction to Literature 3 ____ ENGL 257 Literature of Western Civilization 3 ____ ENGL 258 Literature of Western Civilization 3 ____ ENGL 267 Survey of English Literature 3 ____ ENGL 268 Survey of English Literature 3 ____ ENGL 271 Introduction to Shakespeare 3 (300 L) ____ ENGL 277 Survey of American Literature 3 (300 L) ____ ENGL 278 Survey of American Literature 3 ____ ENGL 285 American Indian Literature 3 (400 L) ____ ENGL 295 Contemp. U.S. Multicultural Literature 3 ____ FLAN 207 Contemporary World Culture 3 ____ INTR 200 Interdisciplinary Seminar 3 ____ PHIL 201 Logic and Critical Thinking 3 Communication – Written: Recognize, send, and respond to written communications for varied audiences as both writer and reader. (LEAP Communication and LEAP Information Literacy) (State Board Core, English Comp) (HS Language Arts - English) Complete 6 credits ____ ENGL 101 ____ ENGL 102 Mathematical and Symbolic Reasoning: Apply mathematical reasoning to investigate and solve problems. (LEAP Quantitative Literacy). (State Board Core, Mathematics) (HS Mathematics) Complete 3-4 credits ____ MATH 123 Contemporary Mathematics 3 ____ MATH 130 Finite Mathematics 4 ____ MATH 143 College Algebra 3 ____ MATH 144 Analytic Trigonometry 2 ____ MATH 147 Pre-Calculus 5 ____ MATH 160 Survey of Calculus 4 ____ MATH 170 Analytic Geometry & Calculus I 4 ____ MATH 175 Analytic Geometry & Calculus II 4 ____ MATH 187 Discrete Mathematics 4 ____ MATH 253 Principles of Applied Statistics 3 ____ MATH 275 Analytic Geometry & Calculus III 4

References Bart, W. (1970). Mathematics Education: The Views of Zoltan Dienes. The School Review, Vol. 78, No. 3. 3. Brownell, W. (1945). The Natural Sciences and Mathematics. Review of Education Research, Vol. 15, No. 4. 4. Brownell, W. (1947). The Place of Meaning in the Teaching of Arithmetic. The Elementary School Journal, Journal, Vol. 47, No. 5. Bruner, J. (1966). Toward a Theory of Instruction. Instruction. W.W. Norton & Company, New York. Bruner, J. (1966). The Culture of Education. Education. Harvard University Press, Cambridge, MA. Bruner, J. (1966). The Process of Education. Education. Harvard University Press, Cambridge, MA. Dienes, Z. (1960). Building Up Mathematics. Mathematics. Hutchinson Educational LTD, London. Hiebert, J, Carpenter, T, & others. (1996). Problem Solving as a Basis for Reform in Curriculum and Instruction: The Case of Mathematics. Educational Researcher, Vol. 25, No. 4. Hiebert, J, Carpenter, T, & others. (2000). Making Sense: teaching and learning mathematics with understanding. understanding. Kilpatrick, J., Wearver, J.F. (1977). The Place of William A. Brownell in Mathematics Education. Journal for Research in Mathematics Education, Vol. 8, No. 5 Noddings, N. (1994). William Brownell and The Search for Meaning. Journal for Research in Mathematics Education, Vol. 24, No. 5. 5. Schoenfeld, A. (1992). Learning to Think Mathematically: Problem Solving, Metacognition, and Sense-Making in Mathematics. Handbook on Research for Mathematics Teaching and Learning. Learning. Schoenfeld, A. (2005). Mathematics Teaching and Learning. . University of California, Berkeley. Learning Skemp, R. (1971). Psychology of Learning Math. Math. Penguin Books Ltd, Harmondsworth. Skemp, R. (1976). Relational Understanding and Instrumental Understanding. Understanding. Mathematics Teaching, 77. 77. Skemp, R. (1987). The Psychology of Knowing Math. Math. Lawrence Erlbaum Associates. Hillsdale, NJ.

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

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

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