This website is a mathematical website
  It presents mathematics, mathematical ideas 
      and reflections on mathematics 




(∀∈>0)(∃δ>0):∣x-x₀∣ < δ ⇒ ∣ψ(x)-ψ(x₀)∣ < ∈ 


 All images on this page are compositions of 2-D surfaces in 3-D space with several tilts and turns



 You are the                Visitor
" MORE THAN 90% OF TOOLS IN GOD'S WORKSHOP ARE MATHEMATHICAL ".
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            HYPER SYMMETRIES-MATHEMATICAL IMAGERY
                                  BY DEJENIE A. LAKEW,PH.D.
                              AUTHORHOUSE, 2009 
           Available also at Major Bookstores : 
         Amazon, Barnes & Nobles, Books-A-Million

It is a book of mathematical images. It can be a gift to your kids, friends or to your self. You will enjoy the images. 
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    My New Mathematical Identities (Verify them) on a new kind of 
     differential operator I defined by:  ∑_{k=0}^{∞}((D^{(k)}/(k!)

    1.  ∑_{k=0}^{∞}((D^{(k)}(cos x))/(k!)) = cos(x+1)
    2.  sin x+∑_{k=1}^{∞}((D^{(k)}(sin x))/(k!)) = sin(x+1)
    3.  ∑_{k=0}^{∞}((D^{(k)}(e^ (x))/(k!)) = e^(x+1)

                                          - Dejenie Alemayehu Lakew
  
    More new results and conjectures on the new operator
   that I defined on the left are posted on my 
   ResearchGate site in Math group under the category:

  Communications in Mathematics Teaching:CMT

  Check it out ! I welcome comments or counter
  examples on the conjectures.
  Definite Integral :

  lim ∑{k=0}ⁿ =∫_{a}^{b}
  n→∞
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                             Dejenie Alemayehu Lakew (Ph.D.)©dejeniea.com, All rights reserved    Powered by Intuit Homestead Technologies   Since 2008
e^{ikπ}±1=0
ℝ   ℂ   Cl_{n}
 ℕ   W   ℤ   ℚ 

 Sett of Numbers: Natural to rationals
Set of Numbers: Reals to Clifford
 Math'l Symbols

  ∈,⊆,⊇
   ∪,∩,∋
  +, -,×,÷,±
  =,≡, ≤, ≥
  ⇒,⇐,⇔
  ∨,∧,∼
  ⇉,⊥,∥
  ∑, ∏ , ∫ 
      
  ∴, ∵, ≅
  MATHEMATICAL IMAGES OF SYMMETRY AND HYPER-SYMMETRY 
Mathematics is both useful and  beautiful
 Les Mathematiques sont dueux utiles et beau
Mathematica est utilis et pulchra
МАТЕМАТИКА одновременно полезные и красивые
מתמטיקה הוא גם שימושי ויפה
الرياضيات هي مفيدة وجميلة
Μαθηματικά είναι τόσο χρήσιμο και όμορφο
Mathematik ist sowohl nützlich als auch beautiful
ሂሳብ በጣም ጠቃሚና ውበት ያለው የጥናትና የምርምር መስክ ነው 
∫_{Ω}φ(((∣u∣)/λ))dx < ∞
MATHEMATICS CONDITIONS US HOW WE THINK AS TECHNOLOGY DOES HOW WE LIVE - DEJENIE A. LAKEW
∄A:ℵ₀<∣A∣<2^{ℵ₀}
∑ → ∫
MATHEMATICS
π

Ψ
{ψ_{k}:k∈ℤ⁺}
 数学是既有用又美观
수학은 유용하고 아름다운 둘 다
 数学は便利で美しい両方です
गणित उपयोगी और सुंदर दोनों है
Wiskunde is beide nuttig en mooi
ریاضیات هر دو مفید و زیبا است

 A mathematician, like a painter or poet, is a maker of patterns. If his patterns are  more permanent than theirs, it is because they are made with ideas.  G. H. Hardy

​Constellation of Analysis 


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  Art and Mathematics
 Mathematics has to be studied not only because it is useful, but because it is also beautiful,       as it is a study of structures of logic and reason - Dr. Dejenie A. Lakew
The Galaxy of Mathematics
Constellation of Algebra
Constellation of Geometry
Gravity of Logic
  Dark Matter  of Imagination 
Stars of Arithmetic and Number Theory
Stars of Algebraic and Differential Geometry
Stars of Topology and Algebraic Topology