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# Math 94: Summer 2023 Rediscovering Mathematics
![[---images/---assets/---icons/important-icon.svg]] **Important links.**
- [[1 teaching/summer program 2023/syllabus|Course syllabus]]
- [[1 teaching/summer program 2023/coding/coding-adventure|Coding adventure]]
The first several weeks will emphasize on geometry, trigonometry, vectors, algebra and polynomials, complex numbers, and the second part of the course will emphasize on calculus, its applications. However, related ideas will cross over to give a more comprehensive view of our mathematical tools. Every week there is also a computer lab component where we would learn how to use Python and spreadsheet programs to solve problems.
$$
\begin{array}{c|c|c|c|c}
\text{Monday} & \text{Tuesday} & \text{Wednesday} & \text{Thursday} & \text{Friday} \\ \hline
& \text{9am -1030am} & & \text{9am -1030am} \\
& \text{Boelter 8251} & & \text{Boelter 8251} \\ \hline
\text{12pm -130pm} & \text{12pm -130pm} & \text{12pm -130pm} & \text{12pm -130pm} & \text{12pm -130pm} \\
\text{Boelter 8251} & \text{Boelter 8251} & \text{Boelter 8251} & \text{Hershey 158} & \text{PIC: MS 2000} \\ \hline
& & & \text{2pm - 4pm} \\
& & & \text{PIC: MS 2000}
\end{array}
$$
MS = Mathematical Science Building
**Week 1 Geometry and trigonometry.**
- **Cosmic distance ladder** - How big is the Earth, the moon, and the Sun? How far are they? Can we figure them out without sophisticated technology?
- [[1 teaching/summer program 2023/week 1/Cosmic_distance_ladder|Worksheet 1: Size of Earth ?]]
- [[1 teaching/summer program 2023/week 1/Cosmic_distance_ladder_2|Worksheet 2: To the Moon...]]
- [[1 teaching/summer program 2023/week 1/Cosmic_distance_ladder_3|Worksheet 3: To the Sun !]]
- [[1 teaching/summer program 2023/week 1/Cosmic_distance_ladder_4|Worksheet 4: Size of Moon ?]]
- [[1 teaching/summer program 2023/week 1/Cosmic_distance_ladder_5|Worksheet 5: Size of the Sun ?!]]
- Supplement: [[1 teaching/summer program 2023/week 1/Pythagorean_theorem_and_orthogonality|Worksheet 6: Pythagorean theorem]]
- Python introduction: Basic operations and types of objects: String, integers, float, list, and dictionary.
- Python introduction: List comprehension and loops. A simple cypher. GATTACA gene.
**Week 2 Geometry and trigonometry**
- **Celestial navigation, latitudes, longitudes, and time.**
- [[1 teaching/summer program 2023/week 2/Celestial_navigation|Worksheet 7: Latitudes]]
- [[1 teaching/summer program 2023/week 2/Celestial_navigation_2|Worksheet 8: North Star and the Southern Cross]]
- [[1 teaching/summer program 2023/week 2/Celestial_navigation_3|Worksheet 9: Axial tilt and is the North Star always the north star?]]
- [[1 teaching/summer program 2023/week 2/Celestial_navigation_4|Worksheet 10: Rotation, sunrise, longitude, and time (TO BE UPDATED).]]
- Supplement: [[1 teaching/summer program 2023/week 2/Trigonometry_cosine_sine|Worksheet 11: Trigonometry, law of cosine, and law of sine (TODO)]]
- Python exercise. Logical statements, functions, and more loops.
- Python exercise. Find the maximum of a function, find the area beneath some curve.
**Week 3 Algebra, logarithms, and exponentials.**
- How to multiply numbers?
- [[1 teaching/summer program 2023/week 3/How-to-multiply-numbers-1|Worksheet : Complex numbers and multiplication]]
- [[1 teaching/summer program 2023/week 3/How-to-multiply-numbers-2|Worksheet : Trigonometric identities, and prosthaphaeresis.]]
- [[1 teaching/summer program 2023/week 3/How-to-multiply-numbers-3|Worksheet : Napier's Logarithms]]
- [[1 teaching/summer program 2023/week 3/How-to-multiply-numbers-4|Worksheet : Applications of logarithms TO BE UPDATED]]
Balancing a chemical equation. Solving linear system of equations.
Determinants and area of a random polygon.
Logarithms and exponentiation. How to multiply really large numbers.
Binomial theorem and the Pascal triangle
Mathematical modeling -- Writing equations of described physical situations.
Python exercise. Find the area of a
Binary expansion of 0.1 and why computers can't handle decimals exactly
Week 4
Derivative rules. Tangent lines and differentiation. Linear approximation.
Optimization using differentiation.
Modeling the world using differential equations. Modeling pendulum motion.
Newton's law of cooling. Murder mystery !
Euler's method to solve differential equations.
Python: Plotting and implementing Euler's method
Python: Plotting and implementing Euler's method
Week 5
Integration technique review
Differential equation hanging rope
Chemical reaction rates
Sequences and series
Power series
Python
Python
Week 6
Power series
Counting and combinatroics
Basic probability
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Group presentation
Group presentation
Group presentation
Additional supplements.
- Pythagorean theorem - How to use yarn to make right angles.
- [[1 teaching/summer program 2023/week 1/Pythagorean_theorem_and_orthogonality|Worksheet]]
- Trigonometry, law of cosine, and law of sine - How to find the height of a mountain.
- [[1 teaching/summer program 2023/week 2/Trigonometry_cosine_sine|Worksheet]]
- Complex numbers and trigonometric identities. - How to multiply using trigonometry.
- Geometry and solving equations - How to trilaterate a position and how many satalites for GPS?
Light beam and reflections - How to put out a fire.
Light beam and refraction - Why does light bends across the water surface?
Rainbow geometry, and UFOs at Rosswell New Mexcio.
Dot product and cross product -- Shape of molecules.
Finding areas and numerical integration.
Week 1
- Day 1. Pythagorean theorem and orthogonality.
- Day 2. Trigonometry basics, as ratios and as functions. Modeling pendulum motion.
- The law of cosine, generalization of Pythagorean theorem.
- Day 3. How to multiply using trigonometry- Trigonometric identities and complex numbers.
- Day 4. Cosmic distance ladder: How big is the Earth? How far is the moon? Can we use sunrise to estimate distances?
- Lab / Discussion. Group work and work sheet / in class introduction of Python : Basic operations and objects. String, integers, floats, lists, and dictionaries.
- Day 5. Lab / Discussion. Group work and work sheet. / Python : Logical statements, loops, and functions. A basic programming paradigm.
Week 2.
- Day 6. The geometry of light beams. Reflection and refraction, Snell's law.
- Day 7. Fermat's principle of least time. How to put out a fire? Idea in optimization using differentiation.
- Rainbow geometry and the story of Rosswell New Mexico's UFO.
- Day 8. Geometry of vectors. Dot product and cross prodcuts. Geometry of chemical molecules.
- Day 9. Numerical integration: Finding areas
- Lab / Discussion. Group work. / Python: Writing functions and loops.
- Day 10. Lab / Discussion. Group work. / Python: Writing functions and loops.
Week 3.
- Day 11. Logarithms and exponentiation. How to multiply really large numbers.
- Day 12. Solving system of linear equation. Balancing chemical equations.
- More on linear system of equations .
- Day 13. Determinants of $2\times 2$ and $3\times 3$ matrices, and higher sizes. What do they mean?
- Day 14. Polynomials, rational functions. Binomial theorem and Pascal triangle.
- Lab / Discussion. Group work. / Python:
- Day 15. Lab / Discussion. Group work. / Python: File I/O, parsing data.
Week 4.
- Day 16. Derivative rules. Tangent lines and differentiation. Linear approximation.
- Day 17. Optimization using differentiation.
- Modeling the world using differential equations. Modeling pendulum motion.
- Day 18. Newton's law of cooling. Murder mystery !
- Day 19. Euler's method to solve differential equations.
- Lab / Discussion. Group work. / Python: Plotting and implementing Euler's method
- Day 20. Lab / Discussion. Group work. / Python: Plotting and implementing Euler's method
Week 5.
- Day 21. How to divide using only addition and multiplication. And how to take the square root.
- Day 22.
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- Day 23.
- Day 24.
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- Day 25. Finding zeros using Newton's method.
Week 6.
- Day 26.
- Day 27.
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- Day 28.
- Day 29.
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- Day 30.
Finding zeros using Newton's method.
Numerical integration: Finding areas
Numerical integration: Solving DE with Euler's method
Where is a billiard ball after a million bounces?
How to divide using only addition and multiplication. And how to take the square root.
Integral table
Activities.
Using yarn to measure 90 degree angles.
Pendulum motion.
How tall is the ceiling, or a mountain top? Using a gravity bob to measure angles.
Projects and presentations.
Week 1
Using yarn to make right angle anywhere.
Paper cut outs to prove Pythagorean theorem.
Using yarn to measure elevation angles.
Week 2
Week 3
Week 4
Week 5
Week 6
Project ideas:
How to estimate the orbital radii of Mercury, Venus, Mars, Jupiter, and Saturn? Greatest elongation, oppositions, and quadrature.
How to find the distance of nearby stars: Parallax.
What about division of complex numbers?
#summer-program-2023