Introduction
From CDS 130
1. Objectives
 To introduce Computational Science, the primary focus of this course.
 To introduce Data Science, which is related to Computational Science.
2. Motivation
 This course is designed to be a first course in computing for scientists.
3. Notes
3.1. Why Computing For Scientists?
 Using computation to solve science problems is as important as
 Using math to solve science problems
 Using a microscope or a telescope to solve science problems
Important: "Computers are used to generate insight, not just numbers"
(The quote appears in Section 1.1 of a book by Hamming)
3.2. What is Computing for Scientists?


3.3. Computational Science
Solving a Computational Science problem requires
 A Scientific Model (A description of the system)
 A Mathematical Model (A translation of the description to a set of mathematical equations)
 Computation (Solving the mathematical equations with a computer)
 Science Analysis and Interpretation
3.4. Relationship to Other Fields
Computational Science
Notes 

An extended discussion of this diagram and the motivation for Computational Science as a discipline is given in [1]. 
3.5. Relationship to Other Fields
Typical questions asked in each discipline:

3.6. Relationship to Other Fields
Data Science (some coverage in this course, in particular visualization)
3.7. Relationship to Other Fields
Typical questions asked in each discipline:

Notes 

Informatics involves the use of information and data to create knowledge. Data Science involves the use of information and data to create scientific knowledge. Both use information technology (tools that enable analysis required to create knowledge). (The term Informatics is often used interchangeably with Data Science, but I use Informatics when I mean the use and analysis of information in a way that has primarily a business or social use as opposed to a scientific use.) For more on Data Science, see [2] and [3]. Informatics and Data Science require core competencies in computing. A few examples of subfields that have arisen over the past decade:
"The flood of data, lack of mechanistic knowledge and the complexity of living systems mean that mathematical modelling and informatics approaches are essential components of modern biology." (Oleg Demin and Igor Goryani in Kinetic Modelling in Systems Biology, Chapman & Hall/CRC, 2009, p. 18) "The science of biology has drastically changed over the last few decades in the sense that it is becoming an increasingly quantitative and progressively less descriptive science" (Ibid, p. 49) 
3.8. Science Models
Recall that solving a Computational Science problem requires
 A Scientific Model (A description of the system)
 A Mathematical Model (A translation of the description to a set of mathematical equations)
 Computation (Solving the mathematical equations with a computer)
 Science Analysis and Interpretation
In the following slides, two models are described: the population model and the harmonic oscillator model.
Notes 


3.9. Population Model
 We will use this model, or variations of it, many times in this course
 To predict the future population, we can make very complex measurements (survey everyone and ask about their plans for reproduction next year, to start) or just use the science model:
Change in population from this year to the next is proportional to number of people this year.
 The mathematical model of the above is
Change in population = aP(this year) P(next year)  P(this year) = aP(this year)
3.10. Population Model Question
A fundamental technique that we will use in this course is iteration. In this example, you will do iteration without a computer. Given the mathematical model,
Change in population = aP(this year) P(next year)  P(this year) = aP(this year)
what is the population two years from now if the population this year is 5 billion and a = 0.1/year, ? Either calculate the answer or state in words how you would do it.
Notes 

P(next year)  P(this year) = a x P(this year) P(next year)  5 = 0.1 x 5 P(next year) = 0.1 x 5 + 5 = 5.5
P(next year)  P(this year) = a x P(this year) P(next year)  5.5 = 0.1 x 5.5 P(next year) = 0.1 x 5.5 + 5.5 = 6.05 
3.11. Harmonic Oscillator Model
 Many problems in engineering can be solved with this model science model:
The force by which an object (such as a spring, certain molecules, stack of paper) pushes back when compressed is proportional to how far the object is compressed.
The mathematical model of this is (k is a number called the "spring constant")
Force pushing back = k·(how far spring is compressed)
Notes 

A model of how a muscle works, how a pendulum swings, and the vibrations of a molecule involves the above mathematical model. Before Newton developed a mathematical model of gravity, Robert Hooke attempted to explain the motion of the planets using this mathematical model. As shown in the animation, a sinusoidal wave is generated by this mathematical model.

3.12. Examples of Scientific Computing
Recall that doing Computational Science requires
 A Scientific Model (A description of the system)
 A Mathematical Model (A translation of the description to a set of mathematical equations)
 Computation (Solving the mathematical equations with a computer)
 Science Analysis and Interpretation
Two models have been discussed: The population model and the harmonic oscillator model. Both the science model and the mathematical model were discussed.
To "do science", we need to do computation and science analysis. Two examples of the four steps of scientific computing are given in the following slides.
 The first example is a model of population for rabbits and wolves. It uses a mathematical model that has components that are similar to the population model.
 The second example is related to galaxy collisions. In this example, the formation of galaxies is studied using Newton's law of gravity.
3.13. Example I of Scientific Computing
The predatorprey problem
3.14. Example I: Science Model
From www.globalchange.umich.edu on June 23 2017 00:10:37.

Assume a closed system (Rabbits and Foxes on an island, for example). Assume the change in number of rabbits per year
Assume that the change in number of foxes per year

3.15. Example I: Mathematical Model
The science model can be written in terms of equations that can be solved using a computer. The mathematical model of the science description stated previously is [6]
ΔR = a·R  b·R·F
ΔF = e·b·R·F  c·F
Where
 R = Number of Rabbits
 F = Number of Foxes
 ΔR = Change in population of rabbits from this year to the next year
 ΔF = Change in population of foxes from this year to the next year
and a, c, b, and e are numbers such as (1.2, 0.5, etc.) and have meaning of
 a is the natural growth rate of rabbits in the absence of predation,
 c is the natural death rate of foxes in the absence of food (rabbits),
 b is the death rate per encounter of rabbits due to predation,
 e is the efficiency of turning predated rabbits into foxes.
Notes 

What you will need to know for this course is that a mathematical model exists, not have a complete understanding of the math involved in solving the problem. After taking this course you will not be able to solve these equations by hand, but you will be able to understand what it means and how to solve it on a computer. 
3.16. Example I: Computation
The very first computation is for
 ΔR = Change in population of rabbits from this year to the next year
 ΔF = Change in population of foxes from this year to the next year
If initially the population was R = 100, F = 10 and you assumed a = 0.1, b = 0.1, c = 0.1, e = 0.1, you would then compute the change in population from year one to year two by plugging in values into the mathematical model equations
ΔR = aR  bRF = 0.1·100  0.1·10·100 = 90
ΔF = ebRF  cF = 0.1·0.1·100·10  0.1·10 = 9
Notes 

Discussion question: What happens when the changes are not integer? (Something similar happens with the population model.) 
3.17. Example I: Science Analysis and Interpretation
Given the results of the simulation, the next steps include answering the following questions:
 What parts of the model are most important? If you leave out parts of the equations, do you get the same answer?
 If one parameter is changed slightly, does the solution change drastically?
 What features of actual measurement do the model explain? What features cannot be explained?
3.18. Example II of Scientific Computing
Galaxy Collisions
3.19. Example II: Science Model
 An initial configuration of galaxy particles (initial positions and velocities)
 Newton's law of gravity
3.20. Example II: Mathematical Model
3.21. Example II: Computation
Need to do this calculation for every combination of mass 1 and mass 2!
Notes 


3.22. Example II: Science Analysis and Interpretation
Given the results of the simulation, the next steps include (see also [8]) answering the following questions:

From science.nationalgeographic.com on June 24 2017 01:20:13.

4. Questions
4.1. Computational Science
Give an example of computational science applied to an scientific discipline. What is the science model that was applied? What was the mathematical model?
4.2. Data Science
Give an example of data science applied to an scientific discipline. What data were used? What analysis was performed?
4.3. Relationship between Data and Computational Sciences
What is the primary relationship between Data Sciences and Computational Sciences?
4.4. Data Science and Computational Science
Give an example of a science problem that is addressed using aspects of both Data Science and Computational Science.