Math & Nature  Geometry & Biology ◦ NGSSS  MA.912.G.4.4: Use properties of congruent and similar triangles to solve problems involving lengths and area.  MA.912.G.5.4: Solve real-world problems involving right triangles.  MA.912.G.7.5: Explain and use formulas for lateral area, surface area, and volume of solids.
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Math & Nature  Geometry & Biology ◦ NGSSS  MA.912.G.4.4 Use properties of congruent and similar triangles to solve problems involving lengths and areas.  MA.912.G.5.3 Use special right triangles (30⁰-60-90⁰ and 45⁰- 45⁰-90⁰) to solve problems.  MA.912.G.7.5 Explain and use formulas for lateral area, surface area, and volume of solids.
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Math & Nature  Geometry & Biology ◦ Geometry Objectives  MA.912.G.7.5 – Explain and use formulas for lateral area, surface area, and volume of solids  MA.912.G.4.4 – Use properties of congruent and similar triangles to solve problems involving lengths and areas  MA.912.G.1.3 – Identify and use the relationships between special pairs of angles formed by parallel lines and transversals
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Math & Nature  Geometry & Biology ◦ NGSSS  MA.912.G.7.5 Explain and use formulas for lateral area, surface area and volume of solids.  MA.912.G.7.7 Determine how changes in dimension affect the surface area and volume of common geometric solids.  MA.912.G.8.2 Use a variety of problem-solving strategies such as drawing a diagram, making a chart, guess-and-check, solve a simpler problem, writing an equation and working backwards.
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Math & Nature  Geometry & Biology ◦ Geometry Objectives  MA.912.G.4.6 Prove that triangles are congruent or similar and use the concept of corresponding parts of congruent triangles.  MA.912.G.6.4 Determine and use measures of arcs and related angles (central, inscribed, and intersections of secants and tangents).
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A Graph Kernel Method for DNA-Binding Site Prediction Changhui Yan* and Yingfeng Wang CS, Utah State U, Logan, UT ABSTRACT: This paper presents a graph kernel method for predicting DNA-binding sites on protein structures. Surface patches are represented using labeled graphs. Then, the graph kernel method is used to calculate the similarities between graphs. A new surface patch is predicted to be interface or non-interface patch based on its similarities to known DNA-binding patches and non-DNA-binding patches. The proposed method achieves 88.7% accuracy, 89.7% specificity, and 87.7% sensitivity when tested on a representative set of 146 protein-DNA complexes using leave-one-out cross-validation. Then, the method is applied to identify DNA-binding sties on 13 unbound structures of DNA-binding proteins. In each of the unbound structure, the top 1 patch predicted by the proposed method precisely indicates the location of the DNA-binding site. Comparisons with other methods confirm the effectiveness of the method. Introduction Structural genomics projects are yielding an increasingly large number of protein structures with unknown function. As a result, computational methods for predicting functional sites on these structures are in urgent demand. There has been significant interest in developing computational methods for identifying amino acid residues that participate in protein-DNA interactions based on combinations of sequence, structure, evolutionary information, and chemical or physical properties. For example, Jones et al. (2003) analyzed residue patches on the surface of DNA-binding proteins and used electrostatic potentials of residues to predict DNA-binding sites. Later, they extended that method by including DNA-binding structural motifs (Shanahan, et al., 2004). In related studies, Tsuchiya et al. (2004) used a structure-based method to identify protein-DNA binding sites based on electrostatic potentials and surface shape, and Keil et al. (2004) trained a neural network classifier to identify patches likely to be DNA-binding sites based on physical and chemical properties of the patches. Neural network classifiers have also been used to identify protein-DNA interface residues based on a combination of sequence and structure information (Ahmad, et al., 2004). Recently, Tjong and Zhou (2007) developed a neural network method for predicting whether a surface residue is in the DNA-binding sites based on the sequence profile of that residue and its structural neighbors. On another track, several methods have been developed for predicting DNA-binding sites using only protein sequence-derived information as input (Ahmad and Sarai, 2005; Wang and Brown, 2006; Yan, et al., 2006). To date, the methods that take the advantage of structure-derived information achieve better results than those using only sequence-derived information. One common limitation of the above-mentioned methods is that the sequence and structural properties of a surface patch are input to machinelearning methods in the form of vectors. When the properties of a surface patch are encoded as a vector, the information of how these properties distribute over the surface is lost. For example, if a surface patch includes five amino acid residues, the above-mentioned methods will encode the amino acid identities of this surface patch as five independent values in a vector. In this representation, the spatial arrangement of these five residues on the surface patch is not encoded. Unfortunately, the spatial arrangement of properties on a surface patch plays a crucial role in determining the function of the surface patch. To overcome this limitation, this paper presents a graphical approach for DNA-binding site prediction. In this study, graphs are used to represent surface patches, such that the spatial arrangement of various properties on the surface is explicitly encoded. The similarities between surface patches are then computed using a graph kernel method. A voting strategy is then used to classify surface patches into DNA-binding sites versus non-binding sites. The proposed method achieves 88.7% accuracy, 89.7% specificity, and 87.7% sensitivity in leave-one-out crossvalidation. When applied to set of unbound structures of DNA-binding proteins, the proposed method can precisely identify the locations of DNA-binding sites.
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More on Triangles Consider ∆ ABC with A (0, 6), B (0, 0), and C (6, 0) and ∆ XYZ with X (6, 3), Y (9, 6), and Z ( 12, 3). Both of these triangles are right triangles. With right angles at B and Y respectively. Find the taxicab lengths of the sides of ∆ ABC. AB* = 6, BC* = 6, AC* = 12 Find the taxicab lengths of the sides of ∆ XYZ. XY* = 6, YZ* = 6, XZ* = 6 Under the correspondence ABC  XYZ are corresponding angles congruent? Under the correspondence ABC  XYZ are corresponding sides congruent? Is SAS satisfied? Are the triangles congruent? 18
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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.
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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
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Rounding Methods Examples Math.ceil(2.1) returns 3.0 Math.ceil(2.0) returns 2.0 Math.ceil(-2.0) returns –2.0 Math.ceil(-2.1) returns -2.0 Math.floor(2.1) returns 2.0 Math.floor(2.0) returns 2.0 Math.floor(-2.0) returns –2.0 Math.floor(-2.1) returns -3.0 Math.rint(2.1) returns 2.0 Math.rint(2.0) returns 2.0 Math.rint(-2.0) returns –2.0 Math.rint(-2.1) returns -2.0 Math.rint(2.5) returns 2.0 Math.rint(-2.5) returns -2.0 Math.round(2.6f) returns 3 Math.round(2.0) returns 2 Math.round(-2.0f) returns -2 Math.round(-2.6) returns -3 8
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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
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Math & Nature  Geometry & Biology ◦ NGSSS  MA.912.G.7.7: Determine how changes in dimension affect the surface area and volume of common geometric solids.  MA.912.G.8.2: Use a variety of problem solving strategies, such as drawing a diagram, making a chart, guess-and-check, solving a simpler problem, writing an equation, and working backwards.
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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. 
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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
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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
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Math & Nature  Geometry & Biology ◦ NGSSS  MA.912.G.8.2 Use a variety of problem-solving strategies, such as drawing a diagram, making a chart, guess-and-check, solving a simpler problem, writing an equation, and working backwards.  MA.912.T.2.1 Define and use the trigonometric ratios (sine, cosine, tangent, cotangent, secant, and cosecant) in terms of angles of right triangles.
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