Martin Flashman's Courses - Math 115 Spring, 2010
Tentative Course Information- Subject to Change (2-25-10)
Algebra and Elementary Functions

MTR     1200 1250  KA 104  
"Lecture 31"  F     1200 1250     BSS_317
"Lecture 32"  F     1400 1450     BSS_317

OFFICE: BSS 356    E-MAIL:        PHONE:826-4950
Hours (Tent.):  MTRF 9:30-10:00      AND BY APPOINTMENT or by CHANCE! [available after class for appointments.]
PREREQUISITE: Math code 40 (or better) or permission. IMPORTANT: You may not need this course to take calculus. MATH PLACEMENT AFTER THE ELM: ALEKS. Click here for Frequently Asked Questions about ALEKS and Math Placement With ALEKS

Catalog Description: In-depth treatment of exponential, logarithmic,trigonometric, and polynomial functions. Prereq: HSU MATH 42 or 44 or 45 or math code 40.
Precalculus: Functions and Graphs - 11e ,Swokowski and Cole,Published by Brooks/Cole.

On-Line Materials: Sensible PreCalculus (Text Notes plus) by M. Flashman
We will cover topics primarily related to theory and application of Functions: Polynomial, Rational, Exponential, Logarithmic, and Trigonometric. Supplementary materials will be provided as appropriate.
  Homework assignments are made regularly. We will use Webassign to assign and grade homework.  Link to Student Quick Start Guide (pdf file).
Homework results should be recorded by 10:00 am of the due date to receive full credit. I will discuss this further at the first class meeting. Assignments will be discussed in class on a daily basis.
The reality check quizzes, some done outside class online and some in-class tests, will have problems similar to assignments and class examples. There will be at least three in-class tests (15-30 minutes) given during the Section meetings.

Section Meetings and Labs:
On Fridays the class will meet in separate sections for which you have registered. These sections meet in a computer lab where we will use the technology to investigate concepts we have been exploring in the larger class meetings. "Lab" assignments will be done in partnerships (at most three people to a partnership) and submitted no later than Wednesday of the next week. The format of the submission will be discussed further in the actual labs. "Lab" time will also be used for brief quizzes and presentations relevant to the lab assignments.
In general you  are expected to attend the" lab" section for which you are registered.
The final examination for the course will be comprehensive.
It is the student's responsibility to request a makeup promptly,
especially for  especially for unauthorized absence.
  • GRADES: Final grades will be determined taking into consideration the quality of work done in the course as evidenced primarily from the accumulation of points from tests and various  assignments.

  • Reality Quizzes 1-7 Best 6 scores 600 points
    Reality Quiz 8 100 points
    Section/Lab assignments 100 points
    Homework 200 points
    Final Examination 400 or 600 points
    Total 1400 or 1600  points
  • The final examination will be be worth either 400 or 600 points determined by the following rule:

  • The final grade will use the score that maximizes the average for the term based on all possible points.
    A grade of less than 50% on the final examination may result in a final grade of  F without offsetting high quality work on the other parts of the course.
  • Notice that only 400 or 600 of these points are from formal in-class examinations, so regular participation is essential to forming a good foundation for your grades as well as your learning.

  • Students with Disabilities: Persons who wish to request disability-related accommodations should contact the Student Disability Resource Center in House 71, 826-4678 (voice) or 826-5392 (TDD). Some accommodations may take up to several weeks to arrange.
    Add/Drop policy: ** See the University rules and dates related to the following: Students are responsible for knowing the University policy, procedures, and schedule for dropping or adding classes.
    Emergency evacuation: Please review the evacuation plan for the classroom (posted on the orange signs) , and review for information on campus Emergency Procedures. During an emergency, information can be found campus conditions at: 826-INFO or
    Academic honesty: Students are responsible for knowing policy regarding academic honesty:
    Attendance and disruptive behavior: Students are responsible for knowing policy regarding attendance and disruptive behavior:

  • Technology: A computer or a graphing calculator can be used for many problems. We will use Winplot and Microsoft Xcel.
  • Graphing Calculators: Graphing calculators are welcome and highly recommended.
  • Use of  Office Hours: Many students find  pre-calculus difficult because of weakness in their algebra background skills and concepts.  A grade of C in Math 44 or intermediate algebra might indicate this kind of weakness.

  • Difficulties that might have been ignored or passed over in previous courses can be a major reason for why things don't make sense now. You may use my office hours for some additional work on these background areas either as individuals or in small groups. My office time is  also available to discuss reality check quizzes, routine problems from homework after they have been discussed in class, as well as using technology.

    Regular use of my time outside of class should be especially useful for students having difficulty with the work and wishing to improve through a steady approach to mastering skills and concepts.
  • Don't be shy about asking for an appointment outside of the scheduled office hours

  • Math 115 Tentative Schedule [Subject to change and correction-4-1-10] 
    Monday Tuesday Thursday
    Friday "Labs"

    I. Introduction: Backgrounds and Key concepts

    1-18 Martin Luther King Day
    No classes.

    1-19 Introduction : How to succeed in this course.

    1-21Sensible Precalc Ch 1.A
    What are Numbers? 
    Comparing Numbers:=,< 

    Introduction to Winplot. Points, Animation..
    Lab #1. 

    II. More Backgrounds:
    Beginning Functions-Linear functions and key concepts. 
    1-25 Number Operations, equations.
    Visualizing: numbers- intervals.
    Solving linear inequalities
    Rational numbers and decimals.
    Sqr(2) is not a rational #. 

    1-26 Applications of linear inequalities
     The Pythagorean theorem.
    Simplifying and Rationalizing
    [Over 30 proofs !]
    [Many Java Applets proofs ]
    Visualizing variables and plane coordinate geometry.
    Plane Coordinates.
    More Geometry review:
    Algebra review.
    Review Polynomials.  (Factoring)
    1-28 Similar triangles.

    Introduction to Excel.
    Linear and quadratic "Functions" and Visualization of data.
    Lab #2.

    III.Functions and lines
    Slopes and equations of lines.
    Midpoints with coordinates.
    Equations for circles.
    Abs. value inequalities

    More on Circles.
    Inequalities and absolute values.
    What's a function?
    On-line Practice Quiz #1?
    More on functions.
    Linear functions.
    Lab #3
    Demonstation: Lines as equations and "functions".
    Exploring functions with Winplot:
    Using winplot to graph and find key function feature and solve equations graphically for zeros. Y and X intercepts.

    IV. Start Trigonometry

    2-8 MORE on functions!
    Graphs and mapping figures.
    Review of Key Triangles.

    Other function qualities.
    Primary Descriptive features of functions. (Increasing/decreasing/max/min) Overview of Core: rational functions.

     Modeling with quadratic functions.

    Lab #4
    Increasing and decreasing functions.
    Secant line slopes.

    V. Triangle Trig
    2-15 Start trig. Trigonometric functions for Right Triangles
    Solving Right triangles.
    Triangle trig: Inverse trig for acute triangles.
    Inverse trig
    More on Solving triangles/ applications.
    Law of sines 
    Law of Sines.
    sine for obtuse angles.

    More Inverse trig (sine obtuse).

    Lab #5
     Graph piecewise functions.
    Visualize triangle trig and unit circle.

    VI.Finish Triangle Trig- Trig function graphs 2-22
    More on Law of Sines.

    Radian measure and circles in general.

    Start Law of cosines.  Lab #6.
    Begin Graphs of trig functions.
    Trig functions for all angles - with radian measure.(sine and cosine)(tan)

    VII Trig Equations 
    Trig Identities
    3-1More on law of cosines.
    A visual proof for "The Law of Cosines" 
    Dynamic proof :The Law of Cosines
    Applications of triangle trig
    Begin Trig Identities 
    Begin trig equations and review of  inverse trig functions(Asin and Acos)
    More on graphs of trig functions, identities and equations.
     Simple use of identities: relating trig function values.
    Solving Simple Trig Equations
    More trig equations and identitiy games.

    Graphs for tangent and secant.  Graphically solving trig equations.

    VIII. More trig identities.:) 3-8 More on Trig Identities:

    More trig equations and identitiy games.

     Addition formulae
    double angles!
    NO Class - University Faculty Furlough

    Spring break [3-12 to 21]

    IX More trig identities, equations, and graphs!
    More Trig functions and equations:
    Addition formulae.
    Double and half angles

    Other Trig identities: Product to sum trig.
    Applications of Sum to slopes and trig function graphs for sine and cosine..

    Quiz #4 Identities and Equations
    Phase Shift - trig and linear compositions.

    X  End of trig!
    3-29 No class
    Flashman Furlough Day

    graphs and elementary functions
    More on graphs and basic properties of trig functions.

    Phase shifts.
    Periodic functions
    On-line Practice Quiz #5 available.
    Phase Shift - trig and linear compositions. Continued!
    LAB #7

    graph SinAX
    graph A sin(BX+C)

    Quiz #5 available on-line. Due 9pm 4-7

    XI Begin Exponential and logs

    4-5Misc. Trig.
    Inverse trig functions.
    More on inverse trig functions(Asin and Acos):
    Graphs for inverse trig. (esp'lly Inverse tangent function)
    More on inverse and trig functions.
    graphs of combining trig functions.
    Exponential Functions.
    Compound interest? What is e?
    Applications of Exponential functions
    Solving simple exponential equations.exponential functions and graphs.
    Graphs of exponential functions.
    More on Exponential Applications- compound interest and growth.
    Exponential graphs
    LAB #8

    XII.Finish exponents and Logarithmic functions.
    What are elementary functions?
    Logarithms: Introduction and definition.

    Basic properties of logs...  and applications and exponents-solving equations
    Models using Exponential Functions
    Continuously compounded interest: Pert.
    More exponential models (Growth/Decay)

    LAB #9
    Logs and Graphs of logs, exps with graphs of trig functions

    XIII. Begin Polynomial and Rational Functions 4-19Logarithmic calculations in equations and computations. "Transforming equations."
    More applications of logs/exponential functions.

    Logarithmic scales
    log scales (simple)
    Log scales
    Quiz #7

    XIV More on rational functions.
    4-26  Long division and factors of polys.
    The remainder Theorem.
    The Factor theorem
    Roots and more on Polynomials.
    Functions The big picture on functions: Core functions and elementary functions
    Symmetry [wrt origin....(axes).]
    Quadratics and 1/x.

    Rational functions.Asymptotes.
    Translation, symmetry and scales for quadratics 
    Difference quotients-Slopes of secant lines-
    for Polynomials.
    Lab #10  Polynomial analysis
    roots and  positive and negative values.
    Roots of polynomials in general - inequalities.

    XVPre-Calculus! 5-3 Inequalities. Linear. Quadratic. Polynomial.

    Quiz #8!
    In Class!
    Quiz # 8 will cover material from the following sections:  TBA
    Absolute value functions and inequalities
    Intermediate value theorem.
    Complex numbers,
    The fundamental theorem of algebra
    Composition & Inverse functions
    Final comments on elementary functions- algebraic, logrithmic exponential, and trignometric.
    Some of my "favorite functions."
    A pre-calculus view of some calculus problems.
    Extremes, tangents,areas.

    Final Exam
    Review Session Sunday
    11:30-1:00 Room BSS


    Inventory of topics:

    Worksheet on log scales
    Music and log scales
    Earthquake Magnitude and logs.
    Slide rules
    On-line java sliderule
    More Slide rules
    More applications of logs
    Trisection of angles, trig and algebra! Complex numbers?
    Complex arithmetic and trig
    Properties of roots and exponents.
    More on Complex Numbers, trig and roots??

    TentativeAssignments on Webassisgn and Recommended Problems Tentative [Subject to change and correction] 
    *Early or Just in time: When two due dates are given,
    the first date is for preparation and/or starting problems,
    the second date is for completion of problem work.

    Last updated: 1-31-10
    Due Date
    Reading Textbook
    or in SC on line.
    Recommended Problems
    Related Graded problems are on WebAssign
    Special Instructions & Interesting but Optional 

    1/22 Sensible Precalc Ch 1.A

    1/22-25 Sensible Precalc Ch 1.B.1 (Firefox Preferred)

    Extra help from Purple Math on Converting between Decimals, Fractions,
       and Percents

    1.1, 1.2 pp 19-26, 1.6 pp 75-79

    More on Similar triangles.
    2/1 Similar triangles.

    Dynamic Geometry® Exploration SimilarTriangles
    2.2: 1-11 odd;23-27 odd; 35,65
    2.3: 1-5; 21-27 odd

    Sensible Precalc Ch 1.B.2 (Firefox preferred)


    2.6: 13-21odd (b and c),41,45,53

    2.7 Examples 3-5.
    2.7: 11-17 odd;37


    Ch 1.B.1:  1c, 2, 16

    Law of Sines.

    A visual proof for "The Law of Cosines"

    Demonstrations of the laws of sines and cosines

    History of Pi

    sin(A+B) proof illustrated.

    Summary of trig identities

    History of Trigonometric functions

    graph SinAX         graph A sin(BX+C)

    Trisection of angles, trig and algebra!
    8.5.3 Multiplying and Dividing Complex Numbers in Trigonometric or Polar Form (Disc 4, 11:08)
    Complex Numbers,

    5.3.3 Graphing Exponential Functions: More Examples (Disc 3, 7:18)

    History of the number e

    How and Why a Slide Rule Works
    On-line java sliderule

    History of the Function concept

    Sensible Precalc Ch 1.B.2 Read!(Firefox preferred)

    Lab #7 0ld.
    old LAB #8 graph SinAX
    graph A sin(BX+C)

    Back to Martin Flashman's Home Page :)
    Back to HSU Math. Department :}