Link to the life stories of four famous mathematicians

Click on this link to read the life stories of Archimedes, Newton, Euler and Gauss.

Topic list for comprehensive final on 7/23

You get two 8.5" x 11" pages of notes, front and back, which means four pages total.

These are the possible topics for the 100 point test.
Binary, decimal hexadecimal
Logical operators, and ^, or v, not ~
Decimals and percents, changing fractions into repeating decimals and vice versa.
Scales other than percents
Scientific notation and rounding to significant digits.
Roman numerals
Fractions in lowest terms
Prime factorizations and all factors
Time: adding subtracting, converting
100 coin problems
simultaneous equations
bels/decibels and Richter scale
Classifications of triangles given angles
Classifications of triangles given sides
Heron’s formula
Area of a triangle with points (0, 0), (a, b) and (c, d)
Distance between points
Pythagorean Theorem
Sets, Venn diagrams, contingency tables and probabilities
Slope of a line and lines with undefined slope
Point-slope form, slope-intercept form
Sum and product problems
Stats: mean, median, mode, five number summary, IQR, outliers
standard deviation, z-scores, z-scores to proportions less than a z-score, reverse lookup table, proportions between two z-scores for a normally distributed set

If something says "formula" or "form", You can expect that formula to be on the test. For things that take methods, like changing from Richter to amount of energy or looking up z-scores, those will not be explained, so they should be in your notes.
 

Finding percentiles from the z-score list. Finding the proportion at an exact number on a list of a normally distributed set

Finding percentiles from the z-score list. 
 One of the things we can do with the z-score to proportion list is find a z-score that corresponds to the cut-off point for a particular percentile. Here are two examples at the 8th percentile and the 80th percentile.

The 8th percentile. because 8 < 50, we will look on the negative z-score side of the sheet. What we want to find is the two positions on the table where the values go from .08xx to .07xx. you will find then in the -1.4 row at the first two positions.

-1.40 -> 0.0808 (8 above 0.0800)
-1.41 -> 0.0793 (7 below 0.0800)

Because 7 < 8, -1.41 counts as the closest to the two, but we should check to see if the average -1.405 would be better. We look at far/close which is 8/7 ~= 1.142857... and if it's less than 3 (it is), we will use the average,so the z-score for the 8th percentile is -1.405.



The 80th percentile. because 80 > 50, we will look on the positive z-score side of the sheet. What we want to find is the two positions on the table where the values go from .79xx to .80xx. you will find then in the 0.8 row in the middle.

0.84 -> 0.7995 (5 below 0.8000)
0.85 -> 0.8023 (23 above 0.8000)

Because 5 < 23, 0.84 counts as the closest to the two, but we should check to see if the average 0.845 would be better. We look at far/close which is 23/5 = 4.6 and if it's more than 3 (it is), we will use the closest instead of the average,so the z-score for the 80th percentile is 0.84.

Finding the proportion at an exact number on a list of a normally distributed set. Consider the SAT values for average mu_x = 500 and sigma_x = 100. SAT scores are always round to the nearest 10, so if we want to find out what percentage of scores are at 600, we have to look at the proportion at 605 and 595.

Raw score 605 become the z-score (605-500)/100 = 105/100 = 1.05, which corresponds to 0.8531

Raw score 595 become the z-score (595-500)/100 = 95/100 = 0.95, which corresponds to 0.8289.

We subtract the small proportion from the big, .8531 - .8289 = .0242. This means about 2.42% of SAT takers will get exactly 600 on one section of the SAT.
 

Links to the five number summary, IQR and outlier material

This link leads to my statistics blog and several examples of the five number summary and how to use it to define outliers.
 

Finding x and y when we are given their sum and product

If we think about a rectangle, the sum of the two adjacent sides is half the perimeter and their product is the area. If we are given the sum and product, can we find the two side lengths? This is the original problem that was being considered when the quadratic formula was derived nearly 900 years ago, though many civilizations before this had something like the idea that is about to be presented.

x + y = sum
xy = product

Let's call half the sum a, which stands for average. Since we are given the sum, a is a known quantity as well. It might be that x = y = a, but generally what is true is we can find a number d, which stands for difference such that

x = a + d
y = a - d

This means the product is the difference of squares, (a + d)(a - d) = a² - d².

Using this, here is how we solve a given problem.

Problem: The sum is 14 and the product is 24.

Solution method: The average a = 7, so we need to solve for d.

(7 + d)(7 - d) = 7² - d² = 49 - d²= 24


Subtract 24 from each side to get

25 - d² = 0

Add d² to both sides to get

 d² = 25.

Take the square root to get d = 5. We use the numbers 7 and 5 in the following way.

7 + 5 = 12
7 - 5 = 2

12 + 2= 14
12 x 2 = 24

With this problem, you could have used guessing and checking to try to find two numbers that added up to 14 (13 and 1, 12 and 2, 11 and 3, no wait, go back to 12 and 2) where the product was 24. let's do one where guessing and checking isn't an option.

Problem: The sum is 15 and the product is 45.

Solution: The average is 7.5 and a² = 56.25. So 56.25 - d²= 45.

Subtracting, we get 11.25 - d²= 0 or d² = 11.25 = 45/4.

Taking square roots, we get d = sqrt(45/4), which simplifies to 3sqrt(5)/2, which rounds to 3.354. Our two numbers are

7.5 + 2sqrt(5)/2 and 7.5 - 2sqrt(5)/2, which round to 10.854 and and 4.146.

More problems of this type.

Problem: The sum is 20 and the product is 40.


Problem: The sum is 40 and the product is 20.


Problem: The sum is 10 and the product is 40.


Problem: The sum is 40 and the product is 10.

Links to material on homework 9, July 13 and 14 2015

Practice to find the equation of a line given two points.

Working with complex numbers.

Links to Venn Diagrams and contigency tables

This link is to a post from my statistics blog about Venn Diagrams and contingency tables.

Prep for midterm 2

Midterm 2 will be based on homeworks 4 through 7 and the biographies of the five British logicians, Boole, Babbage, De Morgan, Dodgson and Lovelace. The most recent posts on this blog from the June 28th post about Richter scale up through the logician biographies will be of the most use in studying.

Links for July 6 and 7 lectures, homework 7 and the five logicians

Here is a link to the life stories of the five British logicians.

Here are practice problems for the interior angle sum and the regular polygon angle measure.

Here are practice problems for changing between different time units.

Here are practice problems for set theory.

If you need more practice, e-mail me and I'll make some more.


 
 

Links to practice problems for distance between two points and area of a triangle defined by three points, one of which is (0, 0)

Here is the link to the practice problems.

More practice
Here are four points. Distances should be given in simplified square root form and approximated to the nearest thousandth,

(0, 0), (6, 3), (10, 1), (-4, -5)

a) Distance from (0, 0) to (6, 3)
b) Distance from (0, 0) to (10, 1)
c) Distance from (0, 0) to (-4, 5)
d) Distance from (6, 3) to (10, 1)
e) Distance from (6, 3) to (-4, -5)
f) Distance from (10, 1) to (-4, -5)

g) the area of the triangle defined by the points (0, 0), (6, 3) and (10, 1)
h) the area of the triangle defined by the points (6, 3), (10, 1) and
(-4, -5)

answers in the comments.
 

Links to triangle classification with angles

Other problems are included, but you can find problems like the homework due on 1 July 2015 on these pages.

Simultaneous equation practice with Kramer's rule

6x + 5y = 18
2x - y = -4

3x + 7y = 12
2x + 5y = -18

Answers in the comments.

100 coin (or ticket) problems

a) 100 coins, all quarters and pennies, total = $13.72

b) 100 tickets, all children ($6) and adult ($12), total =$912

c) 100 coins, all quarters and nickels, total = $8.20

d) 100 coins, all dimes and pennies, total = $3.79

e) 100 coins, all dimes and nickels, total = $7.85

f) 100 coins, all quarters and dimes, total = $14.65

Answers in the comments

The Richter scale: From two readings, the relative strength and vice versa

In class last week, we learned how to find out how much stronger one quake is compared to another given the two Richter scale readings. For example, on June 28, the strongest quake in the U.S. was a 3.4 in Oklahoma, while the strongest in North America was a 5.4 in Niltepec, Mexico. What is the difference in levels of energy? Here are the steps.

Step 1: Subtract little from big. In our case, 5.4 - 3.4 = 2.0.
Step 2: multiply difference by 1.5. 2.0 * 1.5 = 3.0.
Step 3: Raise 10 to the power of the answer from Step 2: 10^3.0 = 1,000. The Mexican quake was 1,000 times stronger than the Oklahoma quake.

Let's ask the question in the opposite direction. Let's say we have a reading for a quake and we know another quake was x times stronger. Again, it will be a three step process, but now we will take the inverse of our three steps above in reverse order. Let's say we have a quake 350 times stronger than the one in Niltepec.  Here are our steps.

Step 1: Take the log of the strength multiplier. Log is the inverse of raising 10 to a power, just like addition is the inverse of subtraction and division is the inverse of multiplication. log(350) = 2.544...,
Step 2: divide the answer from Step 1 by 1.5 and round this answer to the nearest tenth. 2.544/1.5 = 1.696..., which rounds to 1.7. We round to the nearest tenth because the Richter scale rounds to the nearest tenth.
Step 3: Add the answer from Step 2 to the Richter reading we know. In this case, it would be 5.4+1.7 = 7.1, the reading of the stronger quake. If instead we were told a quake was 350 times weaker than Niltepec, it would be 5.4-1.7 = 3.7

Here are some practice questions. The answers are in the comments.

1. 16 times stronger than a 6.1
2. 250 times stronger than a 6.7
3. 8 times weaker than a 5.8

Link to the computer science biographies

Click on this link for the biographies of the five computer scientists. There will be questions on them on the midterm tomorrow.

Links to notes for 22 and 23 June

Notes on changing from decimal to binary and back, binary to hexadecimal and back and decimal to binary and back.

Notes for bitwise operators using binary notation.

Links to notes for 17 and 18 June 2015

Notes for percent and other scales based on powers of 10.

Practice for rates and scientific notation.

Links to all scientific notation posts.

Topics not covered in class that will be covered on Thursday and on homework 2.


Changing repeating decimals to fractions in lowest terms from 2012.

Changing repeating decimals to fractions in lowest terms from 2011. (Different practice problems.)
 


 
 

Links to homework 1, due Wednesday 17 June 2015

Link for prime factorization and all factors, with practice examples.

Roman and Hindu-Arabic numerals, fractions and decimals.

Practice for Roman to Hindu-Arabic and vice versa, fractions and decimals.

Practice for time conversion.

The following problems are in the form minutes:seconds. If the answer gives more than 60 minutes, write the answer as hours:minutes:seconds. Answers to the question below are in the comments.

 18:34
- 6:58


 42:23
 41:07
 43:01
 42:18
+42:17
 
 

Link to the four great mathematician biographies

Here is the link to the biographies of Archimedes, Newton, Euler and Gauss.

Syllabus for Summer 2015

Math 15: Math for Liberal Arts Summer 2015 (L1 30451)
Instructor: Matthew Hubbard
Email: mhubbard@peralta.edu
Text: no required text. If you want a text, personal recommendations can be made
Class website: http://mathlibarts.blogspot.com/
Class hours MTWTh: 10:00 am - 12:05 pm, G-211
Office hours: Math lab G-201
TTh 9:25-9:55 am 3:05-3:35 pm (also available by appointment)
Scientific calculator required (TI-30IIXs, TI-83 or TI-84 recommended)

Important academic schedule dates:
Last date to add, if class is not full: Sat., June 21
Last date to drop class without a "W": Sat. June 21
Last date to withdraw from class: Tues., July 23

Holidays: No holidays this session



Midterm and Finals schedule:

Midterm 1__________Thursday, June 25
Midterm 2__________Thursday, July 9
Comprehensive Final ___Thursday, July 23

Quiz schedule (most Tuesdays and Thursdays) no make-up quizzes given

First week: 6/16 and 6/18                       

Second week: 6/23

Third week: 6/30 and 7/2

Fourth week: 7/7

Fifth week: 7/14 and 7/16

Sixth week: 7/21

Grading Policy
Homework to be turned in: Assigned every Tuesday and Thursday, due the next class
(late homework accepted at the beginning of next class period, 2 points off grade)
If arranged at least a week in advance, make-up midterm can be given.

The lowest two scores from homework and the lowest two scores from quizzes will be removed from consideration before grading.

Grading system
Quizzes 25%* best 2 out of three of these grades
Midterm 1 25%* best 2 out of three of these grades
Midterm 2 25%* best 2 out of three of these grades
Homework 20%
Lab 5%
Final 25%

Anyone who misses less than two homework assignments and gets a higher percentage score on the final than the weighted average of all grades combined will get the final percentage instead deciding the final grade.


Anyone with a class grade of 97% out of all work before the final (this grade will be given on the next to last day) does not have to take the final. That grade is worth an A.

Academic honesty: Your homework, exams and quizzes must be your own work. Anyone caught cheating on these assignments will be punished, where the punishment can be as severe as failing the class or being put on college wide academic probation. Working together on homework assignments is allowed, but the work you turn in must be your own, and you are responsible for checking its accuracy. If I see multiple homework assignments turned in with the exact same wrong answers, I will give a warning. If it happens a second time, the student will get a 0 on the assignment and it will be counted towards the grade.

Class rules: Cell phones and beepers turned off, no headphones or text messaging during class
You will need your own calculator and handout sheets for tests and quizzes. Do not expect to be able to borrow these from someone else.

Student Learning Outcomes

• Analyze an argument for validity using simple rules of logic, and if invalid identify the type of mistake made.
• Compute, with sophisticated formulas, such quantities as interest payments for amortized loans.
• Interpret patterns and draw inferences from them.

Students with disabilities
The Disabled Students Program Services (DSPS) should have your academic accommodation with the instructor. After the first day, I will accept these accommodations electronically or by hard copy on paper. If you need academic accommodation and have not yet applied, please call 510-464-3428 for an appointment.

Exam policies
Quizzes will be closed book and closed notes. Some information you will be expected to remember, other formulas and information will be provided. No sharing of calculators is allowed. You are responsible for knowing how to use your calculator to find answers.

The reciprocal relationship

The teacher will be on time and prepared to teach the class.
The students will be on time and prepared to learn.

The teacher will present the material to the best of his ability.
The students will absorb the material to the best of their ability. They will ask questions when topics are not clear.

The teacher will do his best to answer the questions the students ask about the material, either by repeating an answer with more details included or by taking a different approach to the material that might be clearer to some students.
The students will understand if the teacher feels a topic has been covered enough for the majority of the class and will accept questions being answered outside the class, either in extra time or through written communication.

The teacher will do his best to keep the class about the material. Personal details and distractions that are not germane to the class should not be part of the class.
The students will do their best to keep the class about the material. Questions that are not about the topic should be avoided. Distractions like cell phones and texting are not welcome when the class is in session.

The teacher will give assignments that will help the students master the skills required to pass the course.
The students will put in their best efforts to complete the assignments.
When the assignments are completed, the teacher will make every effort to get the assignments graded and back to the students in a timely manner, by the next class session whenever possible.

The teacher will present real life situations where the skills being learned will be used when they exist. In math, sometimes a particular skill is needed in general to solve later problems that will have real life applications. Other skills have the application of “learning how to learn”, of committing an idea to memory so that committing other ideas to memory becomes easier in the long run.

The student has the right to ask “When will I use this?” when dealing with mathematical topics. Sometimes, the answer is “We need this skill for the next skill we will learn.” Other times, the answer is “We are learning how to learn.” Both of these answers are as valid in their way as “We will need this to understand perspective” or “We use this to balance our checkbooks” or “Ratios can be used to figure out costs” or other real life applications.