- Joshua Thompson teaches mathematics at Rutgers University and has a background in physics. He introduces the different branches of mathematics covered in the course, including arithmetic, algebra, geometry, logic, and applied mathematics. - The class discusses how the ancient Egyptians performed arithmetic using a decimal system based on their ten fingers. Examples are shown of how Egyptians multiplied using the distributive property. - Logic is examined as the foundation of mathematics. It is explained that logic aims to avoid contradictions, and consistency is key in mathematics for formulas to work properly.

1. JOSHUA THOMPSON - 6/13/2020
Introduction into branches of math
CONCEPTSINMATH

2. - Have a degree in Physics with
a math background
- I am trying really hard to get a
PhD in geophysics
- I teach at Rutgers University
You all are way better than
college students
- I love research
JOSHUATHOMPSON
WHO AM I?

3. INTRODUCEYOURSELF!

4. COURSEEXPECTATIONS
Classroom Etiquette
- Ask TONS of questions!
- Respect your peers, instructor, and our class time
Virtual Etiquette
- Keep your video on at all times
- Keep yourself muted until you are ready to speak
- Use the chat box to ask questions, but don’t be shy of the mic!

5. 1. We will always start with a short quiz!
- Don’t Panic! It will not be anything too difficult. I promise
2. Talk about a super famous math person who is not so famous today
- No, not like Einstein.
3. Discuss a branch of math
4. Last, we will do just a little math. Once again…Don’t Panic!
- Many branches of math are just thinking about things
- It doesn’t always involve multiplication or algebra
5. Every student will be expected to talk about math stuff. Don’t be shy!
LEARNINGOBJECTIVES

6. ASKALOTALOTALOTALOTOFQUESTIONS!

7. ASKINGGOODQUESTIONS

8. ASKINGGOODQUESTIONS
What makes a good question?
- Easy to answer
- You get the information you need

9. FORMULATINGQUESTIONS
Tips:
- State what you know
- Guess what the answer might be
- Who/where to ask
- Find a good time
- Research
- Ask yes/no questions

10. - What types or branches of
math do you know?
- What is your favorite thing
about math
BRANCHESOFMATH
LET’S SEE WHAT YOU KNOW

12. BRANCHESOFMATH
- Pure Math
- Arithmetic
- Algebra
- Geometry
- Trigonometry
- Calculus
- Number Theory
- Logic
- Combinatorics
- Topology
- Applied Math
- Dynamical systems and differential
equations
- Mathematical Physics
- Computation
- Information theory and signal processing
- Analysis
- Probability and statistics

13. PUREMATHEMATICS
- The study of mathematical concepts.
- It originated to solve real-world problems. The real obtained for the
pure math calculation is used for practical applications.
- Study of the basic concepts and structures that
underlie mathematics
- This is kinda what this class is about!

14. ARITHMETIC
- Arithmetic is the most ancient branch of mathematics.
- It is used to deal with the numbers i.e., 0 to 9, even odd, prime, or
anything.
- It contains the basic operation to add, subtract, multiply, and divide.
- It is the foundation of pure mathematics!

15. ALGEBRA
- It is one of the main branches of pure math.
- Algebra is a branch of mathematics that substitutes letters for
numbers.
- Algebra is about finding the unknown or putting real-life variables
into equations and then solving them.
- Algebra can include real and complex numbers, matrices, and vectors.

16. GEOMETRY
- Deals with points, lines,
shapes and space.
- Geometry is best
visualized!

17. WHEREDOYOUSTART?

18. DOMATHLIKEANEGYPTIAN:ARITHMETIC
- Long, long ago the early Egyptians settled along the fertile Nile
valley as early as about 6000 BCE
- With a little math…that is 8,000 years ago!
- A decimal numeric system was developed based on our ten fingers.
- The oldest mathematical text from ancient Egypt discovered so far,
though, is the Moscow Papyrus, which dates from the Egyptian
Middle Kingdom around 2000 – 1800 BCE.

19. EGYPTIANNUMBERS

20. LET’STRYTHISOUT.
DO MATH LIKE AN EGYPTIAN

21. EXAMPLES
1. 200
2. 400
3. 30
4. 12
Let’s look at some other examples!
https://math.tools/numbers/to-egyptian/100

22. - The Egyptians used something
called the distributive property
- Can someone describe the
distributive property?
EGYPTIANMULTIPLICATION
DO MATH LIKE AN EGYPTIAN

23. THEDISTRIBUTIVEPROPERTY
JUSTLIKETHEICECREAMCONES!

24. EXAMPLESOFEGYPTIAN
HOWILEARNEDTOMULTIPLY
HOWEGYPTIANMULTIPLY

25. EXAMPLESOFEGYPTIAN
THEEGYPTIANSREALLY
REALLYLIKETHE
DISTRIBUTIVEPROPERTY

26. EXAMPLESOFEGYPTIAN
THEEGYPTIANSREALLY
REALLYLIKETHE
DISTRIBUTIVEPROPERTY

27. - So, the Egyptians used the
distributive property a lot to
make multiplying much much
much easier
EGYPTIANMULTIPLICATION
DO MATH LIKE AN EGYPTIAN

28. LOGIC:THEVERYFUNDAMENTALSOFMATH

29. - Can you describe one thing about
logic
- What does it mean to be logical?
LOGIC

30. LOGIC
- One area of mathematics that has its roots deep in philosophy is the
study of logic.
- Logic is the study of formal reasoning based upon statements or
propositions.
- Logic evolved out of a need to fully understand the details
associated with the study of mathematics.

31. - Logic is trying to have NO contradictions!
- What is a contradiction?
- Can you give an example of contradictions!
CONTRADICTIONS

32. - A contradiction means that something cannot be true and false at the same time.
- Which ones are contradictions?
- A snowy summer's day
- A cold winter’s day
- My sister is jealous of me because I'm an only child.
- Newton is married to Betty, but Betty is not married to Newton.
CONTRADICTIONS

33. MORELOGIC
- Let’s look at some more contradictions!
- If I say people who like cat’s are strange people
- But all my friends are NOT strange
- Then, my friend Timmy says one day, he likes cats

34. MORELOGIC
- Then, Timmy is strange because he likes cats
- But, he is also my friend
- And all my friends are not strange
- So how can Timmy be strange and not strange at the same time!
- AHHHHHHHHHHH!

35. MORELOGIC:CONSISTENCY
- If a statement is consistent, then, there are NO contradictions
- For example,
- All people who like cats are awesome!
- Billy likes cats
- Then, Billy is awesome!
- See how consistency works.

36. MORELOGIC:CONSISTENCY
- If a statement is consistent, then, there are NO contradictions
- For example,
- All people who like cats are awesome!
- Billy likes cats
- Then, Billy is awesome!
- See how consistency works.

37. HOWDOESTHISTIEINTOMATH?

38. - All of math has to be
consistent
- If it wasn’t, then we could not
be confident that 2+2 always
equals 4!
- OR 3 x6 is always 27…..huh?
- I mean 18…
FOUNDATIONSOFMATH
LOGIC AND MATH

39. - We learned how another culture did math
- In future classes we will learn different branches of math
- This means we will learn how math is used in different subjects of science, not different
cultures.
- However, it is interesting to see that math is so important!
- We need math for all sorts of stuff and so have all people in history!
- Logic is needed because math can have no contradictions.
- Math has to always agree
REVIEW

40. - I will ask you the math tool that Egyptians used
- Hint: it is the distributive property
- I will ask you to determine if a sentence is a contradiction.
- That’s it for the quiz next time!
NEXTTIME