MATHEMATICAL CONCEPTS USED IN BIOLOGY (BIOL103/105)

Transcription

1 MATHEMATICAL CONCEPTS USED IN BIOLOGY (BIOL103/105) Mathematical Concepts Concepts in Biol. 103/ Ratio, proportion, percentages Ratio of males to females in a population, ratio of the numbers of predators to preys, ratio of wild type versus mutants in genetic studies, surface area to volume ratio in relation to animal size. Use the number of genetic disease or other various diseases in a population to illustrate the concept of percentage, then convert % into fractions. 2. Averages (arithmetic, geometric mean, weighted average) 3. Algebraic/Arithmetic Expressions (order of precedence of operations) 4. Translate statements into equations (i.e. solve word problems) Use scientific notation to express length and size of organisms, number of cells in an organ. 7. Exponents and Roots including squares and square roots Number of cells after n divisions. 8. Direct or inverse proportionality Proportionality: ( in general) weight and volume (direct proportion), metabolic rate and longevity (inverse proportion). 9. Independent and Dependent variable identification Independent variables are represented on the X-axis, dependent variables on the Y-axis, e.g. rate of reaction (Y-axis) vs temperature or acidity (X-axis). 10. Real World applications of mathematics (particularly for variable identification) Bell shape curve of normal distribution. Log scale is used to plot data of a variable with a huge range e.g. size of smallest animal to largest animal. Use the amplification of a microscope and the stage scale to calculate the actual size of a specimen. 12. Properties of triangles, polygons, circles, parallel and perpendicular lines Mathematical Concepts Concepts in Biol. 103/ Perimeter, surface area, volume Surface area/volume ratio varies with sizes of animals with similar shapes. 16. Understand links between graphical, numerical values, and algebraic expressions 17. Domain, range, intercepts, symmetries, discontinuities, intervals of increase/decrease 22. Probability Probability used in Genetic crosses and predicting outcomes 23. Number of Combinations Use binomial formulae to determine the number of possible combinations, e.g. to find out the number of combinations of 3 heads and 2 tail when tossing 5 coins simultaneously. 24. Distinguish between (and when to use) long division and partial fractions 25. Height and Displacement problems using trigonometry 26. Addition, subtraction and multiplication of matrices 27. Solve linear equations using matrices 28. Statistical concepts (Mean, Median Mode) 29. Statistical concepts (Range, Variation Standard Deviation, and Coefficient of Variation) 30. Statistical concepts (Empirical and theoretical probabilities) 31. Logic Concepts (Making generalizations from cases and analogies related to events) 32. Logic Statements (primitive, implications, disjunctive, and conjunctive; FALSE and TRUE

2 MATHEMATICAL CONCEPTS USED IN BIOLOGY (BIOL104/106) Mathematical Concepts Concepts in Biol. 104/ Ratio, proportion, percentages Surface area to volume ratio, ratio of males and females in a population, ratio of wildt type versus mutants in genetics studies. 2. Averages (arithmetic, geometric mean, weighted average) Average body density of animals with air sacs is lesser in animals without air sacs. 3. Algebraic/Arithmetic Expressions (order of precedence of operations) Calculate heart beat rate by taking the pulse for 15 s. 4. Translate statements into equations (i.e. solve word problems) Length, surface area, and volume of organisms, number of cells in organs and organisms. 7. Exponents and Roots including squares and square roots Number of cells after n divisions. 8. Direct or inverse proportionality Weight and volume show direct proportionality, Inverse proportionality: metabolic rate and longevity; Surface area and puncture force (sharp teeth) ; and thoracic volume and lung pressure. 9. Independent and Dependent variable identification 10. Real World applications of mathematics (particularly for variable identification) 12. Properties of triangles, polygons, circles, parallel and perpendicular lines (Animal design): In comparison to other shapes and forms, Circle encloses largest area with a fixed perimeter length and Sphere encloses largest volume with a fixed surface area. 14. Perimeter, surface area, volume Surface area/volume ratio varies with sizes of animals with similar shapes. 16. Understand links between graphical, numerical values, and algebraic expressions 17. Domain, range, intercepts, symmetries, discontinuities, intervals of increase/decrease Venn diagram to show similarity and differences among the three domains of living organisms. Bilateral and radial symmetries (Classification of animals) All of the following are related to trigonometry: Muscles and forces: compare the forces involved in pushing and pulling a cart. Lever system: compare bone and muscle structures for animals with limbs for running and digging; strategy used to have a wide open mouth (third class levers). Molar teeth are closer to the fulcrum for crushing harder food e.g. nuts. Mathematical Concepts Concepts in Biol. 104/106 Exponential increase in the number of cells in early embryonic development Graphs with log function: response versus log of stimulus (because of the wide stimulus range such as sound frequency and light input). 22. Probability 23. Find out the number of combinations Use binomial formulae to determine the number of possible combinations. Know how a small number of genes encode a large number of antibodies needed for the defense of our body against hundreds of thousands of pathogens. 24. Distinguish between (and when to use) long division and partial fractions 25. Height and Displacement problems using trigonometry 26. Addition, subtraction and multiplication of matrices 27. Solve linear equations using matrices 28. Statistical concepts (Mean, Median Mode) 29. Statistical concepts (Range, Variation Standard Deviation, and Coefficient of Variation) 30. Statistical concepts (Empirical and theoretical probabilities) 31. Logic Concepts (Making generalizations from cases and analogies related to events) 32. Logic Statements (primitive, implications, disjunctive, and conjunctive; FALSE and TRUE 33. Units Show different units with utensils/apparatus, e.g. ruler, spoon, or pipette to show ml, c.c. etc. whenever we have numbers involved with units. For example, 5 million red blood cells per mm 3!! 900 sq feet of surface area in the alveoli of lungs. 34. How to read and use graphs Bell shape curve of normal distribution. Log scale is used to plot data with a huge range e.g. size of smallest animal to largest animal. Understand graphs such as blood pressure and velocity in different types of blood vessels, and in partially blocked blood vessels. Know how to read the Saturation of Hemoglobin with oxygen at different temperatures and ph values.

3 MATHEMATICAL CONCEPTS USED IN MACROECONOMICS (ECON201) Mathematical Concepts Concepts in Macroeconomics 1. Ratio, proportion, percentages Economic Growth, Unemployment, Inflation, Domestic Output 2. Averages (arithmetic, geometric mean, weighted average) Average Propensity to Consume/Save, Average Tax Rate 3. Algebraic/Arithmetic Expressions (order of precedence of operations) The Multiplier Effect, Expenditure Multiplier, Net Export Multiplier 4. Translate statements into equations (i.e. solve word problems) Demand, Supply, and Market Equilibrium GDP, National Debt, Net Export, World Population GDP, National Debt, Net Export 7. Exponents and Roots including squares and square roots 8. Direct or inverse proportionality Demand and Supply Functions, Investment Demand, Demand for Money, Aggregate Demand, Aggregate Supply 9. Independent and Dependent variable identification Demand and Supply, Income and Consumption/Spending, Investment and Real Interest Rate 10. Real World applications of mathematics (particularly for variable identification) Aggregate Expenditure Model, Aggregate Demand / Aggregate Supply Model, Demand and Supply, Recession, Unemployment 12. Properties of triangles, polygons, circles, parallel and perpendicular lines Aggregate Expenditure Model 14. Perimeter, surface area, volume Households as Income Receivers, Household as Spenders, Personal Consumption Expenditure, Ownership of Public Debt, Federal Finance Marginal (Cost Benefit) Analysis, Aggregate Expenditure Model 16. Understand links between graphical, numerical values, and algebraic expressions Production Possibilities Curve or Frontier, Opportunity Cost, Aggregate Expenditure Model 17. Domain, range, intercepts, symmetries, discontinuities, intervals of increase/decrease Business Cycles, Tax Systems, Recession, and Inflation Mathematical Concepts Concepts in Macroeconomics 26. Statistical concepts (Mean, Median Mode) Households as Income Receivers, Personal Distribution of Income, Personal Consumption Expenditure, GDP/Capita for various countries, Taxation (Average Vs. Marginal Tax Rates. 27. Statistical concepts (Range, Variation Standard Deviation, and Coefficient of Variation) 29. Logic Concepts (Making generalizations from cases and analogies related to events)

4 MATHEMATICAL CONCEPTS USED IN PHYSICAL SCIENCE SURVEY I (SCI105) Mathematical Concepts Concepts in Physical Science Survey I (PHYS 105) 1. Ratio, proportion, percentages Density, weight, gas laws, gravitational and Coulomb laws, etc. 2. Averages (arithmetic, geometric mean, weighted average) Experimental data and error analysis 3. Algebraic/Arithmetic Expressions (order of precedence of operations) Relations between physical properties such as time period of a pendulum vs. its length 4. Translate statements into equations (i.e. solve word problems) Relation between velocity, acceleration, time and displacement Avogadro s number, Speed of light, Plank s constant, etc. 7. Exponents and Roots including squares and square roots Centripetal force and speed, gravitational force and distance 8. Direct or inverse proportionality Density vs. volume, Newton s 2nd law of motion, specific heat 9. Independent and Dependent variable identification Graphing data: Speed vs. time 10. Real World applications of mathematics (particularly for variable identification) Cost of electric energy usage: electric heaters, air conditioner, electric bulbs with different powers One dimensional motion. Displacement in simple harmonic motion 12. Properties of triangles, polygons, circles, parallel and perpendicular lines Relation between work, force and displacement. Electromagnetic wave propagation 14. Perimeter, surface area, volume Density, Pressure and force, rotational speed, circular motion Motion in one dimension, Circular motion 16. Understand links between graphical, numerical values, and algebraic expressions Graphing data, extrapolation to make predictions (slope) 17. Domain, range, intercepts, symmetries, discontinuities, intervals of increase/decrease Impulse, heat energy and temperature change Distinguish between (and use) irrational and rational functions Mathematical Concepts Concepts in Physical Science Survey I (SCI 105) 26. Statistical concepts (Mean, Median Mode) 27. Statistical concepts (Range, Variation Standard Deviation, and Coefficient of Variation) Experimental data error analysis 29. Logic Concepts (Making generalizations from cases and analogies related to events) Physical laws

5 MATHEMATICAL CONCEPTS USED IN PHYSICAL SCIENCE SURVEY II (SCI106) Mathematical Concepts Concepts in Physical Science Survey II (PHYS 106) 1. Ratio, proportion, percentages Conversions, Kepler s laws 2. Averages (arithmetic, geometric mean, weighted average) Experimental data and error analysis 3. Algebraic/Arithmetic Expressions (order of precedence of operations) Relations between physical properties such as Relative humidity, Maximum capacity, and actual moisture content 4. Translate statements into equations (i.e. solve word problems) Atmospheric pressure at higher altitudes Avogadro s number, Speed of light, Plank s constant, etc. Brightness of stars 7. Exponents and Roots including squares and square roots Kepler s laws 8. Direct or inverse proportionality The gas laws, star distances and parallax 9. Independent and Dependent variable identification Graphing data: gas pressure vs. time at fixed volume 10. Real World applications of mathematics (particularly for variable identification) Seasons - temperature predictions, place and time, landscape - topology Celestial coordinates (distance, declination, and right ascension 12. Properties of triangles, polygons, circles, parallel and perpendicular lines Determining zenith angle and altitude angle of sun 14. Perimeter, surface area, volume Sizes of astronomical objects 16. Understand links between graphical, numerical values, and algebraic expressions Graphing data, extrapolation to make predictions (atmospheric layers, lapse rate) 17. Domain, range, intercepts, symmetries, discontinuities, intervals of increase/decrease Lapse rate and atmospheric temperature Distinguish between (and use) irrational and rational functions Mathematical Concepts Concepts in Physical Science Survey II (SCI 106) 26. Statistical concepts (Mean, Median Mode) 27. Statistical concepts (Range, Variation Standard Deviation, and Coefficient of Variation) Experimental data error analysis 29. Logic Concepts (Making generalizations from cases and analogies related to events) Physical laws