16
Lectures
45
minutes/lecture
1.
The Language of Music
Professor Greenberg begins the course with an introduction to one of the musical language's key syntactical elements—timbre, or the actual sound or tone color of an instrument or instruments—beginning with the string section of the orchestra.
1.
The Language of Music
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9.
Intervals and Tunings
Resuming you focus on pitch, you will turn once more to Pythagoras, and his investigation into what is now known as the overtone series. This paves the way for an examination of intervals, the evolution of tuning systems, and an introduction to the major pitch collections.
9.
Intervals and Tunings
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2.
Timbre, Continued
His exploration of timbre continues with plucked string instruments and woodwinds—both single- and double-reeds—as well as a discussion of the concept of transposing instruments and dynamics.
2.
Timbre, Continued
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10.
Tonality, Key Signature, and the Circle of Fifths
This lecture explains the concept of a tonal center, or tonic, discusses how musical keys are constructed and how they relate to one another. It also introduces a fundamental graphic and conceptual aid in understanding keys and their relationships—the circle of fifths.
10.
Tonality, Key Signature, and the Circle of Fifths
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3.
Timbre, Part 3
You conclude our discussion of timbre with the brass and percussion families before moving on to the evolution of the orchestra from the early 17th to the 20th centuries.
3.
Timbre, Part 3
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11.
Intervals Revisited and Expanded
An interval is the relationship between two pitches, and can range from the most simple in terms of acoustical ratio, where the two pitches blend well, to the most acoustically complex, where the pitches blend poorly. This lecture explores that range, from the simplest—the consonant, stable octave—to the most complex—the dissonant and unstable tritone.
11.
Intervals Revisited and Expanded
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4.
Beat and Tempo
A simple definition of music offered in Lecture 1 was "sound in time." Moving from our exploration of the "sound" aspect of music, we now begin an exploration of the role of "time" in music.
4.
Beat and Tempo
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12.
Melody
Begin with an examination of the single most important aspect of music: melody. Here you will look at the four basic types of thematic melody: word melody, vocal melody, vocally conceived instrumental melody, and instrumental melody; and continue with an examination of musical motives and motivic development, and the function of motives in creating melody.
12.
Melody
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5.
Meter, Part 1
Meter refers to how individual beats are grouped in a given passage. This lecture considers two basic types, duple meter and triple meter, the "dance meter" of which the waltz is the most enduring and popular example.
5.
Meter, Part 1
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13.
Melody, Continued
This lecture reviews and builds on the analysis of thematic melody begun in the previous lecture. Instrumental melody is discussed, along with other types of melody, including accompanimental melody, countermelody, periodic melody, and continuous melody.
13.
Melody, Continued
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6.
Meter, Part 2
Examine some of the ways a composer can manipulate the listener's sense of beat and meter, including syncopation, compound meter, additive meter, and asymmetrical meter.
6.
Meter, Part 2
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14.
Texture and Harmony, Part 1
The idea of texture in music—the number of different melody lines in a given section of music and their relationship to one another—is introduced by discussing the four basic musical textures: monophony, polyphony, homophony, and heterophony.
14.
Texture and Harmony, Part 1
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7.
Pitch and Mode, Part 1
After three lectures of discussion about the "time" aspect of music—rhythm—you will return to its sound aspect, introducing and defining terms such as noise, fundamental frequency, pitch, pitch collection, note, melody, harmony, interval, octave, and overtone and Pythagoras's role in "discovering" the overtone series.
7.
Pitch and Mode, Part 1
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15.
Harmony, Part 2—Function, Tendency, and Dominance
Functional tonality is the tonal system that dominated Western music from the 16th to the 20th centuries. It is at its heart about tension and release. This lecture discusses the roles of various harmonies.
15.
Harmony, Part 2—Function, Tendency, and Dominance
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8.
Pitch and Mode, Part 2
Professor Greenberg continues his discussion of pitch and mode with a focus on the essential building block of the Western pitch systems—the octave—and its importance in tonal music. In this lecture you will also explore musical modes.
8.
Pitch and Mode, Part 2
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16.
Harmony, Part 3—Progression, Cadence, and Modulation
Professor Greenberg concludes with the concepts of harmonic progression, the movement from one chord to the next; cadence, the progressions that serve as musical punctuation marks; and the techniques of modulation, by which a composer can change keys during the course of a movement.
16.
Harmony, Part 3—Progression, Cadence, and Modulation
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24
Lectures
30
minutes/lecture
1.
The Joy of Math—The Big Picture
Professor Benjamin introduces the ABCs of math appreciation: The field can be loved for its applications, its beauty and structure, and its certainty. Most of all, mathematics is a source of endless delight through creative play with numbers.
1.
The Joy of Math—The Big Picture
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13.
The Joy of Trigonometry
Trigonometry deals with the sides and angles of triangles. This lecture defines sine, cosine, and tangent, along with their reciprocals, the cosecant, secant, and cotangent. Extending these definitions to the unit circle allows a handy measure of angle: the radian.
13.
The Joy of Trigonometry
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2.
The Joy of Numbers
How do you add all the numbers from 1 to 100—instantly? What makes a square number square and a triangular number triangular? Why do the rules of arithmetic really work, and how do you calculate in bases other than 10?
2.
The Joy of Numbers
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14.
The Joy of the Imaginary Number i
Could the apparently nonsensical number the square root of –1 be of any use? Very much so, as this lecture shows. Such imaginary and complex numbers play an indispensable role in physics and other fields, and are easier to understand than they appear.
14.
The Joy of the Imaginary Number i
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3.
The Joy of Primes
A number is prime if it is evenly divisible by only itself and one: for example, 2, 3, 5, 7, 11. Professor Benjamin proves that there are an infinite number of primes and shows how they are the building blocks of our number system.
3.
The Joy of Primes
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15.
The Joy of the Number e
Another indispensable number to learn is e = 2.71828 ... Defined as the base of the natural logarithm, e plays a central role in calculus, and it arises naturally in many spheres of mathematics, including calculations of compound interest.
15.
The Joy of the Number e
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4.
The Joy of Counting
Combinatorics is the study of counting questions such as: How many outfits are possible if you own 8 shirts, 5 pairs of pants, and 10 ties? A trickier question: How many ways are there to arrange 10 books on a shelf? Combinatorics can also be used to analyze numbering systems, such as ZIP Codes or license plates, as well as games of chance.
4.
The Joy of Counting
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16.
The Joy of Infinity
What is the meaning of infinity? Are some infinite sets "more" infinite than others? Could there possibly be an infinite number of levels of infinity? This lecture explores some of the strange ideas associated with mathematical infinity.
16.
The Joy of Infinity
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5.
The Joy of Fibonacci Numbers
The Fibonacci numbers follow the simple pattern 1, 1, 2, 3, 5, 8, etc., in which each number is the sum of the two preceding numbers. Fibonacci numbers have many beautiful and unexpected properties, and show up in nature, art, and poetry.
5.
The Joy of Fibonacci Numbers
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17.
The Joy of Infinite Series
Starting with the analysis of the proposition 0.999999999 ... = 1, this lecture exÂplores what it means to add up an infinite series of numbers. Some infinite series conÂverge on a definite value, while others grow arbitrarily large.
17.
The Joy of Infinite Series
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6.
The Joy of Algebra
Arguably the most important area of mathematics, algebra introduces the powerful idea of using an abstract variable to represent an unknown quantity. This lecture demonstrates algebra's golden rule: Do unto one side of an equation as you do unto the other.
6.
The Joy of Algebra
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18.
The Joy of Differential Calculus
Calculus is the mathematics of change, and answers questions such as: How fast is a function growing? This lecture introduces the concepts of limits and derivatives, which allow the slope of a curve to be measured at any point.
18.
The Joy of Differential Calculus
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7.
The Joy of Higher Algebra
This lecture shows how to solve quadratic (second-degree) equations from the technique of completing the square and the quadratic formula. The quadratic formula reveals the connection between Fibonacci numbers and the golden ratio.
7.
The Joy of Higher Algebra
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19.
The Joy of Approximating with Calculus
Exploiting the idea of the derivative, we can approximate just about any function using simple polynomials. This lecture also shows why a formula sometimes known as "God's equation" (involving e, i, p, 1, and 0) is true, and how to calculate square roots in your head.
19.
The Joy of Approximating with Calculus
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8.
The Joy of Algebra Made Visual
Algebra can be used to solve geometrical problems, such as finding where two lines cross. The technique is useful in real-life problems, for example, in choosing a telephone plan. Graphs help us better understand everything from lines to equations with negative or fractional exponents.
8.
The Joy of Algebra Made Visual
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20.
The Joy of Integral Calculus
Geometry and trigonometry are used to determine the areas of simple figures such as triangles and circles. But how are more complex shapes measured? Calculus comes to the rescue with a technique called integration, which adds the simple areas of many tiny quantities.
20.
The Joy of Integral Calculus
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9.
The Joy of 9
Adding the digits of a multiple of 9 always gives a multiple of 9. For example: 9 x 4 = 36, and 3 + 6 = 9. In modular arithmetic, this property allows checking answers by "casting out nines." A related trick: mentally computing the day of the week for any date in history.
9.
The Joy of 9
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21.
The Joy of Pascal's Triangle
A geometric arrangement of binomial coefficients called Pascal's triangle is a treasure trove of beautiful number patterns. It even provides an answer to the song "The Twelve Days of Christmas": Exactly how many gifts did my true love give to me?
21.
The Joy of Pascal's Triangle
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10.
The Joy of Proofs
Professor Benjamin begins his discussion of mathematical proofs with intuitive cases like "even plus even is even" and "odd times odd is odd." He builds to more complex proofs by existence and induction, and ends with a checkerboard challenge.
10.
The Joy of Proofs
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22.
The Joy of Probability
Mathematics can draw detailed inferences about random events. This lecture covers major concepts in probability, such as the law of large numbers, the central limit theorem, and how to measure variance.
22.
The Joy of Probability
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11.
The Joy of Geometry
Geometry is based on a handful of definitions and axioms involving points, lines, and angles. These lead to important conclusions about the properties of polygons. This lecture uses geometric reasoning to derive the Pythagorean theorem and other interesting results.
11.
The Joy of Geometry
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23.
The Joy of Mathematical Games
This lecture applies the law of total probability and other concepts from the course to predict the long-term losses to be expected from playing games such as roulette and craps and understand what is known as the "Gambler's Ruin Problem."
23.
The Joy of Mathematical Games
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12.
The Joy of Pi
Pi is the ratio of the circumference of a circle to its diameter. It starts 3.14 and continues in an infinite nonrepeating sequence. Professor Benjamin shows how to learn the first hundred digits of this celebrated number, making it look as easy as pie.
12.
The Joy of Pi
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24.
The Joy of Mathematical Magic
Closing the course with a magician's flair, Professor Benjamin shows a trick for producing anyone's phone number, how to create a magic square based on your birthday, how to play "mathematical survivor," a technique for computing cube roots in your head, and a card trick to ponder.
24.
The Joy of Mathematical Magic
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24
Lectures
30
minutes/lecture
1.
A Sequence of Words
Building great sentences depends on more than just stringing words together. This lecture explores the definition of a sentence and introduces several assumptions on which the course rests, such as that a greater control of syntax is one of the most direct routes to improving writing.
1.
A Sequence of Words
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13.
The Riddle of Prose Rhythm
Follow along with scholars and critics as they try to study, measure, and explain the mystery of prose rhythm. Learn to better recognize the distinctive rhythms that characterize your sentences by imagining their modifying levels as long or short bits of Morse code.
13.
The Riddle of Prose Rhythm
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2.
Grammar and Rhetoric
Examine some of the key terminology used throughout the course and focus on learning how sentences work (their rhetoric) instead of merely labeling their constituent parts (their grammar).
2.
Grammar and Rhetoric
|
14.
Cumulative Syntax to Create Suspense
Learn to start thinking about sentences as not just "loose" or "periodic" but as possessing degrees of suspense. Base clauses in a cumulative sentence can be moved about or split to increase or decrease the reader's suspense about how the sentence will end.
14.
Cumulative Syntax to Create Suspense
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3.
Propositions and Meaning
A sentence may contain more propositions than are visible in the grammar and syntax of its surface language. Discover how the facts, ideas, and feelings in a sentence lie beneath its words and organization.
3.
Propositions and Meaning
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15.
Degrees of Suspensiveness
In this lecture, you unpack the periodic/suspensive sentence, which suggests a greater degree of control over its material and, when used effectively, can generate interest by combining complex concepts with syntactical suspense.
15.
Degrees of Suspensiveness
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4.
How Sentences Grow
Adding propositional content to a kernel sentence ("They slept.") moves sentences forward and enriches their meaning. Here are three types of strategies that give sentences more momentum and depth: the connective, the subordinative, and the adjectival.
4.
How Sentences Grow
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16.
The Mechanics of Delay
Look closely at four broad tactics to delay completing the base clause, two of which involve the manipulation of modifiers and two of which use initial clauses or phrases as either extended subjects or as modifiers. You also consider a possible fifth tactic that involves using a colon or semicolon.
16.
The Mechanics of Delay
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5.
Adjectival Steps
Professor Landon makes the case for using adjectival strategies to increase the efficiency and effectiveness of your sentences. Boiling down subordinate clauses to single modifying words allows you to pack more information into each sentence.
5.
Adjectival Steps
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17.
Prefab Patterns for Suspense
Another option for adding suspense to sentences is starting them with certain prompts such as "if" or "since." This lecture illustrates the uses of these and other prompts and considers some reasons for making suspense a critical part of your prose style.
17.
Prefab Patterns for Suspense
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6.
The Rhythm of Cumulative Syntax
Cumulative sentences lend themselves to writing moves that almost guarantee more effective sentences. Learn how these easy-to-write sentences take you through increasingly specific sentence levels and how they clarify and embellish preceding phrases.
6.
The Rhythm of Cumulative Syntax
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18.
Balanced Sentences and Balanced Forms
Perhaps the most intense form of the periodic/suspensive sentence is the balanced sentence. Professor Landon points out that balanced sentences, in drawing their strength from the tension between variation and repetition, offer an advantage to writers comparing two subjects.
18.
Balanced Sentences and Balanced Forms
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7.
Direction of Modification
Cumulative sentences also employ modifying words and phrases before, between, or at the end of base clauses. Investigate the benefits and potential risks of each of these placement options on the meaning of your sentences.
7.
Direction of Modification
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19.
The Rhythm of Twos
Binary oppositions in balanced sentences lend confidence and conclusiveness to writing. With its mirroring effect, the duple (double-beat) rhythm gives balanced sentences the power to stay lodged in your mind.
19.
The Rhythm of Twos
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8.
Coordinate, Subordinate, and Mixed Patterns
With your newfound understanding of the relationship between base clauses and modifying phrases, you examine the three major patterns of cumulative sentences and their effect on the base clause: coordinate (refining information), subordinate (providing new information), and mixed (combining the previous two patterns).
8.
Coordinate, Subordinate, and Mixed Patterns
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20.
The Rhythm of Threes
Three-part series bring an extended balance to sentences through the buildup of elements in threes. Delve into the unity, progression, and intensification at the heart of this syntactical form.
20.
The Rhythm of Threes
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9.
Coordinate Cumulative Sentences
This lecture elaborates on coordinate cumulative patterns, which pile up modifying phrases that point back to the base clause. It also emphasizes the importance of listening to how your sentences read as a means of tightening up their logic.
9.
Coordinate Cumulative Sentences
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21.
Balanced Series and Serial Balances
Sentence balance is an extension of the organizational constructs of human consciousness. Explore the prevalence of balanced rhythm in our speech and writing and look at numerous examples of sentence balance.
21.
Balanced Series and Serial Balances
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10.
Subordinate and Mixed Cumulatives
Continuing the discussion of various cumulative sentence patterns, Professor Landon zeroes in on subordinate and mixed patterns, which offer more variety to sentences by adding specificity or tapping into the strengths of both coordinate and subordinate patterns.
10.
Subordinate and Mixed Cumulatives
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22.
Master Sentences
The opposite of the minimal base clause is the master sentence: a very long sentence that can function in remarkably original and controlled ways. While no formula can anticipate the context and purpose of master sentences, you can construct effective ones by combining a number of the strategies from earlier lectures.
22.
Master Sentences
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11.
Prompts of Comparison
Prompts like "as if," "as though," and "like" can prompt writers to look for metaphors, similes, or speculative phrases that add information, clarification, and imaginative appeal to sentences. Learn how writers forge emotional links with their readers by incorporating figurative language into their writing.
11.
Prompts of Comparison
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23.
Sentences in Sequence
Move beyond the sentence and on to the impact of several sentences in sequence and see new possibilities of resonance and relationship among their rhythms and structures.
23.
Sentences in Sequence
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12.
Prompts of Explanation
Prompts can also speculate about the unknown. Examine three major prompts—"because," "perhaps," and "possibly"—to use in your sentences, so you can reveal more of your thinking and strengthen the connection between you and your readers.
12.
Prompts of Explanation
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24.
Sentences and Prose Style
How do our sentences fit into prose style? In exploring critical approaches to this issue, Professor Landon emphasizes that prose style can be seen as both a problem and a gift passed on from writer to writer.
24.
Sentences and Prose Style
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24
Lectures
30
minutes/lecture
1.
Making High-Stakes Decisions
Examine the myth that bad decisions are most often made by bad leaders. Professor Roberto uses the examples of the Challenger disaster, the Bay of Pigs invasion, and Daimler's acquisition of Chrysler to uncover why good leaders can make bad decisions if the decision-making process they use is flawed.
1.
Making High-Stakes Decisions
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13.
Creativity and Brainstorming
IDEO is one of the world's leading product design firms, expert in developing creative and innovative products for many industries. What makes their process so effective? To help you understand their formula at work, Professor Roberto describes an experiment in which IDEO staff worked to design a new product in just one week.
13.
Creativity and Brainstorming
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2.
Cognitive Biases
Using the story of the tragedies on Mount Everest in 1996, Professor Roberto introduces you to three cognitive biases that play a role in bad decision making: sunk-cost effect, overconfidence bias, and recency effect.
2.
Cognitive Biases
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14.
The Curious Inability to Decide
Often as individuals or in groups we become paralyzed by indecision—unable to commit to one path or another. This lecture examines three modes of indecision in groups: "the culture of yes, the culture of no, and the culture of maybe."
14.
The Curious Inability to Decide
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3.
Avoiding Decision-Making Traps
Explore more decision-making traps you can fall into if you're not aware of them, such as confirmatory bias, anchoring bias, attribution error, illusory correlation, hindsight bias, and egocentrism. Darwin avoided confirmatory bias by keeping a separate record of observations that contradicted his theory of evolution.
3.
Avoiding Decision-Making Traps
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15.
Procedural Justice
Using case studies about Daimler Chrysler and an aerospace and defense firm, Professor Roberto explains the challenge of building consensus among team members once a decision has been made so everyone will work together to implement it.
15.
Procedural Justice
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4.
Framing—Risk or Opportunity?
The way you or others frame a problem or decision can have a significant impact on the choices you make. Understand why framing a decision in terms of what you have to lose causes you to take more risks.
4.
Framing—Risk or Opportunity?
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16.
Achieving Closure through Small Wins
To move forward through the brainstorming and decision-making processes, groups must find intermediate moments of agreement that Karl Weick calls "small wins." This lecture looks at how teams achieve closure through small wins, using cases about D-Day, Social Security, and the CEO of Corning.
16.
Achieving Closure through Small Wins
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5.
Intuition—Recognizing Patterns
Discover how to use intuition as a powerful tool in decision making when combined with rational analysis and acknowledge the cognitive processes that are part of our intuition. Professor Roberto recounts case studies from firefighting, health care, and the video game industry to explain the potential and pitfalls of intuition.
5.
Intuition—Recognizing Patterns
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17.
Normal Accident Theory
Discover how organizational culture and structure affect decision making by individuals and groups. Learn about the Three Mile Island accident to understand what went wrong in that system, and understand how catastrophes more often stem from a domino chain of bad decisions rather than one wrong choice.
17.
Normal Accident Theory
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6.
Reasoning by Analogy
Learn how the Korean War differed from the threat of Adolf Hitler. Professor Roberto explains reasoning by analogy and how you can use analogies to make sense of a complex problem. At the same time, we must avoid the common tendency to overstate the similarities of one situation to another and overlook key differences.
6.
Reasoning by Analogy
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18.
Normalizing Deviance
The tragic explosion of the Challenger space shuttle was likely the result of a flawed culture at NASA. The repeated and increased tolerance of questionable data and decisions ultimately led to a large-scale failure. How can leaders reform such cultures?
18.
Normalizing Deviance
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7.
Making Sense of Ambiguous Situations
We might like to think that we carefully examine our choices before we make a decision. However, we often do the reverse—make a decision and then figure out why, and base future decisions on how we made sense of other decisions. This process, called sense-making by Karl Weick, constantly influences our behavior.
7.
Making Sense of Ambiguous Situations
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19.
Allison's Model—Three Lenses
Learn Graham Allison's approach to examine decision making through three lenses. Use Allison's model to explore the Cuban Missile Crisis from the individual and cognitive perspective, the group dynamics view, and the vantage point of organizational politics and bargaining.
19.
Allison's Model—Three Lenses
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8.
The Wisdom of Crowds?
This lecture includes examples from game shows such as Who Wants to Be a Millionaire? and from the business world that demonstrate the usefulness of decision making by groups and the potential problems if group members are not fully engaged.
8.
The Wisdom of Crowds?
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20.
Practical Drift
Uncover why organizations make decisions that contradict their own rules and regulations. The concept of practical drift explains this phenomenon, as you see by studying a military friendly-fire case from 1994.
20.
Practical Drift
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9.
Groupthink—Thinking or Conforming?
Discover why even diverse groups can make bad decisions if members are not able to express divergent opinions. This lecture focuses on how groupthink led to the Bay of Pigs invasion.
9.
Groupthink—Thinking or Conforming?
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21.
Ambiguous Threats and the Recovery Window
When a threat is ambiguous, organizations are likely to minimize the possible risks. Look again at NASA but this time at the Columbia space shuttle accident, 17 years after the Challenger explosion, to understand how conditions changed or stayed the same in that culture.
21.
Ambiguous Threats and the Recovery Window
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10.
Deciding How to Decide
After the Bay of Pigs failure, President Kennedy and his advisors reflected on their mistakes and created a new process for group discussion and decision making to prevent future groupthink and promote diverse perspectives. Here, Professor Roberto introduces the concept of developing a decision-making process.
10.
Deciding How to Decide
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22.
Connecting the Dots
Often in large organizations, no one individual can see or understand all the elements at the same time. Great organizations integrate various pieces to see the big picture. Discover how failure to connect the dots led to an inability to recognize the extent of the threat of a terrorist attack on American soil and therefore a lack of appropriate action before September 11.
22.
Connecting the Dots
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11.
Stimulating Conflict and Debate
Learn how constructive conflict can lead to new insights and stronger decisions. Discover four methods to stimulate useful debate: role plays, mental simulation techniques, creating a point-counterpoint dynamic, and applying diverse conceptual models and frameworks.
11.
Stimulating Conflict and Debate
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23.
Seeking Out Problems
Explore how complex, high-risk organizations succeed by focusing on the possibility of failure. Leaders at these organizations proactively look for problems rather than ignore red flags. Also, learn how Toyota's application of these principles has contributed to its success.
23.
Seeking Out Problems
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12.
Keeping Conflict Constructive
Unfortunately, it's not uncommon for conflict to become unproductive. Understand how to look for and eliminate dysfunctional conflict to cultivate effective teams. This lecture includes cases on Sid Caesar's comedy writing team, health care, and the nonprofit sector.
12.
Keeping Conflict Constructive
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24.
Asking the Right Questions
Examine the trend of leaders moving from making decisions themselves to focusing on how decisions are made by everyone in their organizations. Smart leaders, as you discover, ask the right questions to glean the collective wisdom of their colleagues and staffs.
24.
Asking the Right Questions
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