The Great Courses

Does the celebrated harmonic series diverge or converge? Discover a proof using the integral test. Then generalize to define an entire class of series called p-series, and prove a theorem showing when they converge. Close with the sum of the harmonic series, the fascinating Euler-Mascheroni constant, which is not known to be rational or irrational.

Why does emotion emerge in mammalian evolution and what role does the emotion of awe play in human development? Dr. Dacher Keltner takes you on an exploration of what scientists have discovered about the cross-cultural universality of awe and its physical, mental, and social benefits - and specific ways in which you can experience awe more often in your own life.

Author and former professional baseball player Mike Robbins brings a unique perspective to the workplace. As a baseball player, he noticed that the most successful teams were not necessarily those with the greatest individual talent but those with the greatest chemistry and support between players. Gain techniques to help you create that chemistry and support in the workplace.

Chances are you have a lot of positive experiences in your life right now. But are they fleeting - do you even truly notice them? Learn how a mindfulness practice can help you convert positive experiences into long-term beneficial traits, through self-correcting positive neuroplasticity, what Rick Hanson calls "the superpower of superpowers."

Dr. Siegel shares his guided mindfulness meditation called "Wheel of Awareness." With this practice, you'll learn to integrate four main aspects of life and mind: the five senses, internal bodily sensations, mental activity and emotions, and relationship to the outside world. More than 10,000 individuals have integrated these four aspects of the life of the mind to create better mental health.

Recent scientific discoveries reveal not only the mechanisms of aging at the cellular level, but also how our mental activities affect those processes. With Dr. Elissa Epel, learn how your activities can affect inflammation; the health of our mitochondria, our cells' centers of energy production; and our epigenome, the chemical compounds that turn our genes on and off.

In this session with Dr. Shapiro, open by engaging in a meditation exercise to gather intention and center yourself in the present moment. Explore common questions about mindfulness, from concerns about maintaining focus to dealing with feelings of tiredness and even physical pain, and learn how to begin your own mindfulness practices and how to set goals you can commit to.

We're always glad to be mindful of our emotions of gratitude, awe, or joy. But what about anger? With Juna Mustad, learn why our normal reactions to anger - either allowing it to drive our actions or stuffing it deep inside - are unhealthy. Learn how to become mindful of your anger, and how that awareness can point you to a healthier, more authentic life and better relationships with others.

Our minds include our subjective experience, consciousness, and information processing. But how does this all come together? With Dr. Siegel, learn why self-organization is one of the key attributes of all complex systems. Discover how that quality of integration predicts the quality of mental health, and how the practice of mindfulness can take us to healthy integration.

Our ability to pay attention and stay focused on a task is incredibly important for our productivity and safety - and often the safety of others. But the attention system in our brain is easily affected by our moods and stress. Are there exercises we can do to train our brain? And, if so, does that training show benefits over time? Dr. Amishi Jha explores brain training from a new perspective.