MATHEMATICAL CONCEPTS USED IN BIOLOGY (BIOL103/105)
Mathematical Concepts
1. Ratio, proportion, percentages
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Averages (arithmetic, geometric mean, weighted average)
Algebraic/Arithmetic Expressions (order of precedence of operations)
Translate statements into equations (i.e. solve word problems)
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Scientific Notation (i.e. 5.6x10 is 5.6e-3 or 8.4x10 is 8.4e+6)
Properties of Real Numbers and their representation on number line
Exponents and Roots including squares and square roots
Direct or inverse proportionality
9. Independent and Dependent variable identification
10. Real World applications of mathematics (particularly for variable identification)
11. Distance between two points and the midpoint of a line segment
12. Properties of triangles, polygons, circles, parallel and perpendicular lines
13. Height and Displacement problems using geometry
Mathematical Concepts
14. Perimeter, surface area, volume
15. Equations for straight lines, circles, and parabolas
16. Understand links between graphical, numerical values, and algebraic expressions
17. Domain, range, intercepts, symmetries, discontinuities, intervals of increase/decrease
18. Distinguish among (and use) various types of polynomials
19. Distinguish between (and use) trigonometric functions
20. Distinguish between (and use) exponential functions and logarithmic functions
21. Distinguish between (and use) irrational and rational functions
22. Probability
23. Number of Combinations
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
statements)
Concepts in Biol. 103/105
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.
Use scientific notation to express length and size of organisms, number of cells in an organ.
Number of cells after n divisions.
Proportionality: ( in general) weight and volume (direct proportion), metabolic rate and longevity (inverse
proportion).
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).
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.
Concepts in Biol. 103/105
Surface area/volume ratio varies with sizes of animals with similar shapes.
Probability used in Genetic crosses and predicting outcomes
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.
MATHEMATICAL CONCEPTS USED IN BIOLOGY (BIOL104/106)
1.
2.
3.
4.
5.
6.
7.
8.
Mathematical Concepts
Ratio, proportion, percentages
Averages (arithmetic, geometric mean, weighted average)
Algebraic/Arithmetic Expressions (order of precedence of operations)
Translate statements into equations (i.e. solve word problems)
Scientific Notation (i.e. 5.6x10-3 is 5.6e-3 or 8.4x106 is 8.4e+6)
Properties of Real Numbers and their representation on number line
Exponents and Roots including squares and square roots
Direct or inverse proportionality
9. Independent and Dependent variable identification
10. Real World applications of mathematics (particularly for variable identification)
11. Distance between two points and the midpoint of a line segment
12. Properties of triangles, polygons, circles, parallel and perpendicular lines
13.
14.
15.
16.
17.
Height and Displacement problems using geometry
Perimeter, surface area, volume
Equations for straight lines, circles, and parabolas
Understand links between graphical, numerical values, and algebraic expressions
Domain, range, intercepts, symmetries, discontinuities, intervals of increase/decrease
18. Distinguish among (and use) various types of polynomials
19. Distinguish between (and use) trigonometric functions
Mathematical Concepts
20. Distinguish between (and use) exponential functions and logarithmic functions
Concepts in Biol. 104/106
Surface area to volume ratio, ratio of males and females in a population, ratio of wildt type versus mutants in genetics studies.
Average body density of animals with air sacs is lesser in animals without air sacs.
Calculate heart beat rate by taking the pulse for 15 s.
Length, surface area, and volume of organisms, number of cells in organs and organisms.
Number of cells after n divisions.
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.
(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.
Surface area/volume ratio varies with sizes of animals with similar shapes.
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.
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).
21. Distinguish between (and use) irrational and rational functions
22. Probability
23. Find out the number of combinations
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 statements)
33. Units
34. How to read and use graphs
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.
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 mm3!! 900 sq feet of surface area in the alveoli of lungs.
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.
MATHEMATICAL CONCEPTS USED IN MACROECONOMICS (ECON201)
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5.
6.
7.
8.
Mathematical Concepts
Ratio, proportion, percentages
Averages (arithmetic, geometric mean, weighted average)
Algebraic/Arithmetic Expressions (order of precedence of operations)
Translate statements into equations (i.e. solve word problems)
Scientific Notation (i.e. 5.6x10-3 is 5.6e-3 or 8.4x106 is 8.4e+6)
Properties of Real Numbers and their representation on number line
Exponents and Roots including squares and square roots
Direct or inverse proportionality
9. Independent and Dependent variable identification
10. Real World applications of mathematics (particularly for variable identification)
11.
12.
13.
14.
Distance between two points and the midpoint of a line segment
Properties of triangles, polygons, circles, parallel and perpendicular lines
Height and Displacement problems using geometry
Perimeter, surface area, volume
15. Equations for straight lines, circles, and parabolas
16. Understand links between graphical, numerical values, and algebraic expressions
17. Domain, range, intercepts, symmetries, discontinuities, intervals of increase/decrease
18. Distinguish among (and use) various types of polynomials
19. Distinguish between (and use) trigonometric functions
Mathematical Concepts
20. Distinguish between (and use) exponential functions and logarithmic functions
21. Distinguish between (and use) irrational and rational functions
22. Distinguish between (and when to use) long division and partial fractions
23. Height and Displacement problems using trigonometry
24. Addition, subtraction and multiplication of matrices
25. Solve linear equations using matrices
26. Statistical concepts (Mean, Median Mode)
27. Statistical concepts (Range, Variation Standard Deviation, and Coefficient of Variation)
28. Statistical concepts (Empirical and theoretical probabilities)
29. Logic Concepts (Making generalizations from cases and analogies related to events)
30. Logic Statements (primitive, implications, disjunctive, and conjunctive; FALSE and TRUE
statements)
Concepts in Macroeconomics
Economic Growth, Unemployment, Inflation, Domestic Output
Average Propensity to Consume/Save, Average Tax Rate
The Multiplier Effect, Expenditure Multiplier, Net Export Multiplier
Demand, Supply, and Market Equilibrium
GDP, National Debt, Net Export, World Population
GDP, National Debt, Net Export
Demand and Supply Functions, Investment Demand, Demand for Money, Aggregate
Demand, Aggregate Supply
Demand and Supply, Income and Consumption/Spending, Investment and Real Interest
Rate
Aggregate Expenditure Model, Aggregate Demand / Aggregate Supply Model, Demand
and Supply, Recession, Unemployment
Aggregate Expenditure Model
Households as Income Receivers, Household as Spenders, Personal Consumption
Expenditure, Ownership of Public Debt, Federal Finance
Marginal (Cost Benefit) Analysis, Aggregate Expenditure Model
Production Possibilities Curve or Frontier, Opportunity Cost, Aggregate Expenditure
Model
Business Cycles, Tax Systems, Recession, and Inflation
Concepts in Macroeconomics
Households as Income Receivers, Personal Distribution of Income, Personal Consumption
Expenditure, GDP/Capita for various countries, Taxation (Average Vs. Marginal Tax Rates.
MATHEMATICAL CONCEPTS USED IN PHYSICAL SCIENCE SURVEY I (SCI105)
1.
2.
3.
4.
5.
6.
7.
Mathematical Concepts
Ratio, proportion, percentages
Averages (arithmetic, geometric mean, weighted average)
Algebraic/Arithmetic Expressions (order of precedence of operations)
Translate statements into equations (i.e. solve word problems)
Scientific Notation (i.e. 5.6x10-3 is 5.6e-3 or 8.4x106 is 8.4e+6)
Properties of Real Numbers and their representation on number line
Exponents and Roots including squares and square roots
8. Direct or inverse proportionality
9. Independent and Dependent variable identification
10. Real World applications of mathematics (particularly for variable identification)
11. Distance between two points and the midpoint of a line segment
12. Properties of triangles, polygons, circles, parallel and perpendicular lines
13. Height and Displacement problems using geometry
14. Perimeter, surface area, volume
15. Equations for straight lines, circles, and parabolas
16. Understand links between graphical, numerical values, and algebraic expressions
17. Domain, range, intercepts, symmetries, discontinuities, intervals of increase/decrease
18. Distinguish among (and use) various types of polynomials
19. Distinguish between (and use) trigonometric functions
20. Distinguish between (and use) exponential functions and logarithmic functions
Distinguish between (and use) irrational and rational functions
Mathematical Concepts
22. Distinguish between (and when to use) long division and partial fractions
23. Height and Displacement problems using trigonometry
24. Addition, subtraction and multiplication of matrices
25. Solve linear equations using matrices
26. Statistical concepts (Mean, Median Mode)
27. Statistical concepts (Range, Variation Standard Deviation, and Coefficient of Variation)
28. Statistical concepts (Empirical and theoretical probabilities)
29. Logic Concepts (Making generalizations from cases and analogies related to events)
30. Logic Statements (primitive, implications, disjunctive, and conjunctive; FALSE and TRUE
statements)
Concepts in Physical Science Survey I (PHYS 105)
Density, weight, gas laws, gravitational and Coulomb laws, etc.
Experimental data and error analysis
Relations between physical properties such as time period of a pendulum vs. its length
Relation between velocity, acceleration, time and displacement
Avogadro’s number, Speed of light, Plank’s constant, etc.
Centripetal force and speed, gravitational force and distance
Density vs. volume, Newton’s 2nd law of motion, specific heat
Graphing data: Speed vs. time
Cost of electric energy usage: electric heaters, air conditioner, electric bulbs with
different powers
One dimensional motion. Displacement in simple harmonic motion
Relation between work, force and displacement.
Electromagnetic wave propagation
Density, Pressure and force, rotational speed, circular motion
Motion in one dimension, Circular motion
Graphing data, extrapolation to make predictions (slope)
Impulse, heat energy and temperature change
Concepts in Physical Science Survey I (SCI 105)
Experimental data error analysis
Physical laws
MATHEMATICAL CONCEPTS USED IN PHYSICAL SCIENCE SURVEY II (SCI106)
Mathematical Concepts
1. Ratio, proportion, percentages
2. Averages (arithmetic, geometric mean, weighted average)
3. Algebraic/Arithmetic Expressions (order of precedence of operations)
4.
5.
6.
7.
Translate statements into equations (i.e. solve word problems)
Scientific Notation (i.e. 5.6x10-3 is 5.6e-3 or 8.4x106 is 8.4e+6)
Properties of Real Numbers and their representation on number line
Exponents and Roots including squares and square roots
8. Direct or inverse proportionality
9. Independent and Dependent variable identification
10. Real World applications of mathematics (particularly for variable identification)
11. Distance between two points and the midpoint of a line segment
12. Properties of triangles, polygons, circles, parallel and perpendicular lines
13. Height and Displacement problems using geometry
14. Perimeter, surface area, volume
15. Equations for straight lines, circles, and parabolas
16. Understand links between graphical, numerical values, and algebraic expressions
17. Domain, range, intercepts, symmetries, discontinuities, intervals of increase/decrease
18. Distinguish among (and use) various types of polynomials
19. Distinguish between (and use) trigonometric functions
20. Distinguish between (and use) exponential functions and logarithmic functions
Distinguish between (and use) irrational and rational functions
Mathematical Concepts
22. Distinguish between (and when to use) long division and partial fractions
23. Height and Displacement problems using trigonometry
24. Addition, subtraction and multiplication of matrices
25. Solve linear equations using matrices
26. Statistical concepts (Mean, Median Mode)
27. Statistical concepts (Range, Variation Standard Deviation, and Coefficient of Variation)
28. Statistical concepts (Empirical and theoretical probabilities)
29. Logic Concepts (Making generalizations from cases and analogies related to events)
30. Logic Statements (primitive, implications, disjunctive, and conjunctive; FALSE and TRUE
statements)
Concepts in Physical Science Survey II (PHYS 106)
Conversions, Kepler’s laws
Experimental data and error analysis
Relations between physical properties such as Relative humidity, Maximum capacity, and
actual moisture content
Atmospheric pressure at higher altitudes
Avogadro’s number, Speed of light, Plank’s constant, etc.
Brightness of stars
Kepler’s laws
The gas laws, star distances and parallax
Graphing data: gas pressure vs. time at fixed volume
Seasons - temperature predictions, place and time, landscape - topology
Celestial coordinates (distance, declination, and right ascension
Determining zenith angle and altitude angle of sun
Sizes of astronomical objects
Graphing data, extrapolation to make predictions (atmospheric layers, lapse rate)
Lapse rate and atmospheric temperature
Concepts in Physical Science Survey II (SCI 106)
Experimental data error analysis
Physical laws