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I'm not okay and you're not okay. We're in serious trouble. And yet the life that we are promised in Christ should be one of spiritual maturity and increasing holiness. We should be light and salt to a dark and flavourless world. We should be brimful of the fruit of the Spirit. So, why the yawning chasm between what we are and what we should be? When around half of marriages fail, when there are massive problems with addiction, when our leaders are moral failures, when there is war and world famine, who can we blame? Only ourselves, says Dallas Willard. We live from the heart - the spiritual place within us from which outlook, choices and actions have been formed by a world away from God. Now it must be transformed. With piercing cultural analysis Dallas Willard shows how the spirit of the age has blinded Christian people to the truth of their moral responsibilities. He presents a radical challenge to be transformed to the likeness of Christ in every dimension of life - thought, emotion, character, soul and body. Drawing on biblical and practical resources he explores the spiritual disciplines that are crucial if, by the grace of God, we hope to acquire renovated hearts.
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This elegant book by distinguished mathematician John Milnor, provides a clear and succinct introduction to one of the most important subjects in modern mathematics. Beginning with basic concepts such as diffeomorphisms and smooth manifolds, he goes on to examine tangent spaces, oriented manifolds, and vector fields. Key concepts such as homotopy, the index number of a map, and the Pontryagin construction are discussed. The author presents proofs of Sard's theorem and the Hopf theorem.