MathBench Australia Biology Modules
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NAVIGATION
Measurement
Basic Lab Techniques
1: Metric Review
2: Choose your weapon
3: Read your weapon
4: Can you read this pipette?
5: Summary
Straight Lines/ Standard Curves
1: Line graphs
2: Straight lines
3: A straight line has only one slope
4: Slopes and spectros
5: Standard curve-the wavelength
6: Standard curve-making and using
7: Beer’s Law
8: The plug and chug method
9: Try a biology example
10: Summary
Logs and pH
1: When size matters
2: There must be a better way!
3: The log is the power!
4: What about other numbers?
5: And what about SMALL numbers?
6: Your turn with other numbers
7: Antilogs
8: Measuring the power of an earthquake
9: Measuring acidity
10: Differences in acidity: Here are two problems
11: Summary
Calculating Molar Weight
1: What is a mole?
2: How much does a mole weigh?
3: Molar weights made easy
4: …but not quite that easy
5: Using the Periodic Table
6: Water
7: Practice with sulfuric acid
8: …and caffeine
9: Going backwards
10: …and rubies
11: Summary
The Size of Things
1: Tall (and small) tales
2: Metric conversions: step to the right, step to the left
3: 3 Worlds: Milli, Micro, Nano
4: Focus on the microworld
5: Practise measuring in the microworld
6: Next stop … the nanoworld
7: End of the line… the picoworld
8: Summary
Visualisation
A Graphing Primer
1: The case of the confusing axes
2: Choose your x and y carefully
3: Practise labelling the axes
4: Next step: ranging the axes
5: Practise ranging the axes
6: Next step: scale the axes
7: Practise determining labelled interval distance
8: How to scale axes
9: Finally fill in the axes
10: Summary
Log Transformations
1: Logs of graphs and Graphs of logs
2: Method 1: log then graph
3: The curvy line turned into a straight line!
4: To transform or not to transform?
5: Method 2: graph then log
6: Graphing bigger (and smaller) numbers
7: Try it out
8: Just add realism
9: Summary
Chopping up Plasmids
1: Three thieves and a beaded necklace
2: And the moral is?
3: A real plasmid
4: Practice with restriction sites
5: What’s wrong with these gels?
6: Playing with plasmids
7: Other weird things
8: Summary
Cellular Processes
Introduction to Diffusion
1: Measuring movement
2: Directed vs undirected movement
3: Measuring movement using flux
4: Gradients and diffusion
5: Visualising the gradient
6: Fick’s First Law
7: The gradient in Fick’s First Law
8: A familiar equation for Fick’s First Law
9: Graphing Fick’s First Law
10: How does flux depend on distance?
11: A fragrant example
12: General transport equations and Fick’s First Law
13: Summary
Time to Diffuse
1: Fick’s second law: … is about “time to diffuse”
2: A very useful formula
3: Time-to-diffuse increases dramatically
4: General functions and Diffusion
5: Biological applications
6: Why do rhinos have lungs and amoebas don’t?
7: Diffusion is efficient in small organisms but not big ones
8: Why we have lungs
9: How many macrophages does it take to kill a virus?
10: You need a lot of macrophages – or one smart one!
11: Summary
Diffusion through a Membrane
1: Review of diffusion equations
2: The two-compartment model
3: What does continuous mean?
4: Examples of permeability
5: A formula for permeability
6: The area of the membrane
7: The final equations
8: Rate of flux
9: A metaphor
10: Continuous curves
11: Discrete curves
12: Iterating the discrete curve
13: Summary
Osmosis
1: Osmosis is a special kind of diffusion
2: Putting the Os into Osmolarity
3: Calculating osmolarity
4: Osmolarity adds up
5: Which way will water flow?
6: …and how fast?
7: What else can the equations tell us?
8: Where does it all end?
9: Drink your water
10: Sharks, alligators and goldfish
11: Summary
The Nernst Potential
1: Getting through membranes
2: Going with the flow
3: Permeability is key!
4: Meet the neighbourhood
5: Getting groovy with gradients
6: Some real numbers
7: The Goldman Equation
8: Playing with the Goldman Equation
9: The Nernst Equation
10: Taking Nernst for a test drive
11: More about Nernst
12: How about those logs?
13: Pumps and channels
14: At equiliubrium? Or far from it?
15: Opening the gate
16: The action potential and the Goldman equation
17: Action potential and the Nernst equation
18: Summary
Microbiology
Matt’s Holiday Nightmare
1: What causes cholera?
2: Build the basic growth equation
3: Draw exponential growth
4: How long until 1 million bacteria?
5: All we need now is data
6: Looking at data
7: Log transformation straightens out exponential growth
8: Do ALL curves get “straightened” by taking the log?
9: Phases of bacterial growth
10: A test for exponential growth
11: And the answer is…
12: To recap
13: Some more practice
14: Extended problem: Exponential growth ends
15: Summary
Matt Gets Messy: In search of Exact Doubling Time
1: In search of … the exact doubling time
2: Finding doubling time with general numbers
3: Logarithms = Exponent-busters
4: Now let’s try out our knowledge of logs
5: More exponent busting
6: World Population
7: Growth of technology
8: How long before the oysters are unsafe?
9: Summary
Methods for Counting Bacteria
1: Recap the story
2: Count them all?
3: Direct count
4: Light scatter (spectrophotometer)
5: The dilemma of the dead cell
6: Viable plate count
7: Comparison of methods
8: Summary
Viable Plate Count… or how to count to a million
1: Why we need to dilute
2: Setting the stage: Diluting Cold Press Coffee
3: Working out the dilution
4: Overall dilution
5: Design a dilution scheme
6: How to scale up
7: Count a plate!
8: Why we plate more than one dilution?
9: Picking the plate to count
10: Putting it all together
11: Quickies
12: Is the water safe?
13: Summary
Probability and Statistics
Normal Distributions and the Scientific Method
1: The Scientific Method
2: What makes a Good Procedure?
3: Normal Fish
4: More about normal distributions
5: Visualising a normal distribution
6: Testing Fish2Whale
7: Exploring the Fish2Whale Distribution
8: Overlapping Distributions
9: Summary: The End for now…
Bar Graphs and Standard Error
1: Beyond the scatterplot
2: Practice with quantitative and qualitative
3: How to make a bar chart
4: How to make a fancier bar chart
5: Info lost and found
6: Error bars
7: Practice with error bars
8: And another way: the standard error
9: The same graph both ways
10: Summary
BLAST and (Im)probability
1: Combinatorics
2: Combining letters into words
3: Many names for large numbers
4: Four-letter alphabet
5: How many base sequences?
6: How many AA sequences?
7: Division
8: How many ways can you make a protein?
9: To be or not to be… in blast
10: Blast: do try this at home
11: Summary
Basic Rules of Probability
1: Introduction
2: All Life’s a Game
3: The Law of OR
4: Some Fine Prints
5: What if you violate the fine print?
6: More game shows
7: What are the chances?
8: The Law of AND
9: More fine prints
10: Examples of independent events
11: What if you violate the fine print?
12: Summary
13: Practice with dice
14: Practice with coins
15: What else can probability do?
16: To Curl or not to Curl
17: Surviving the numbers game
18: Gaining an edge
19: Hanging on for dear life
Mice with Fangs: Intro to Punnett Squares
1: Introduction
2: The Punnett Menu
3: Creating combinations Chez Punnett
4: Insults by the dozen
5: Punnett menu revisited
6: Onwards to Genetics
7: Recap of genetics vocab
8: Can this marriage be saved?
9: Vampire fangs
10: Example: Mr Spock and Jax
11: Example: Mr Spock and Nurse Chapel
12: And you thought we were done!
13: The dreaded double hybrid
14: Another dihybrid cross
15: Summary
More Mice with Fangs: Intermediate Punnett Squares
1: Introduction
2: A Punnet Insult Generator
3: Quick Recap of Genetics Vocab
4: Reviewing the Dreaded Double Hybrid
5: Not all double crosses are dihybrids!
6: Ms Heterozygote meets Mr Recessive
7: Fuzzy meets Fangy
8: Back to Probability
9: Really big Punnett Squares
10: Summary
Statistical Tests
Chi-squared Tests
1: Do those shoes fit?
3: The day is saved … or not
2: Dilbert’s three-day work week
7: What’s a p-value?
8: What’s a Lookup Table?
4: What you observe vs what you expect
5: The chi-squared equation
6: Give it a try
Goodness of Fit Tests
1: Do those shoes fit?
2: Dilbert’s 3 day work week
3: The day is saved . or not
4: The Brute Force method
5: Computer = brute force
6: What’s your threshold for pain?
7: Sick-day sistribution
8: A brief recap of the Brute Force Method
9: The Brute Force method again
10: Using arithmetic instead of Brute Force
11: One small correction
12: How big is big?
13: Degrees of Freedom
14: The magic lookup table
15: The answer, finally
16: Summary of chi-square
17: Another example for chi-square
18: So, which method do you like better?
19: Applications
20: Example 1: Testing for a dihybrid ratio
21: Example 2: Habitat selection (ecology)
22: Review and Words of Wisdom
Testing Differences with the T-Test
1: How to convince your boss
2: Looking at the data
3: Estimating averages
4: How do we measure variation? If you said standard deviation…
5: How accurate are our estimates?
6: Combining errors
7: Getting to t-calc
8: A general formula for t-calc
9: Degrees of freedom
10: The bottom line (finally)
11: Give it a try
12: Once more for luck
13: The big picture
